Some Sources on "Participating in the American Death Penalty" by Rabbi Kalmanofsky
(ו) שֹׁפֵךְ֙ דַּ֣ם הָֽאָדָ֔ם בָּֽאָדָ֖ם דָּמ֣וֹ יִשָּׁפֵ֑ךְ כִּ֚י בְּצֶ֣לֶם אֱלֹקִ֔ים עָשָׂ֖ה אֶת־הָאָדָֽם׃

(6) Whoever sheds human blood,
By human [hands] shall that one’s blood be shed;
For in the image of God Was humankind made.

"The Guilt of the murder is infinite because the murdered life is invaluable...the effect of this view is, to be sure, paradoxical: because human life is invaluable, to take it entails the death penalty."
Moshe Greenberg, Some Postulates in Biblical Criminal Law

(ו) וְהַנָּבִ֣יא הַה֡וּא א֣וֹ חֹלֵם֩ הַחֲל֨וֹם הַה֜וּא יוּמָ֗ת כִּ֣י דִבֶּר־סָ֠רָה עַל־ה' אֱלֹֽקֵיכֶ֜ם הַמּוֹצִ֥יא אֶתְכֶ֣ם ׀ מֵאֶ֣רֶץ מִצְרַ֗יִם וְהַפֹּֽדְךָ֙ מִבֵּ֣ית עֲבָדִ֔ים לְהַדִּֽיחֲךָ֙ מִן־הַדֶּ֔רֶךְ אֲשֶׁ֧ר צִוְּךָ֛ ה' אֱלֹקֶ֖יךָ לָלֶ֣כֶת בָּ֑הּ וּבִֽעַרְתָּ֥ הָרָ֖ע מִקִּרְבֶּֽךָ׃

(6) As for that prophet or dream-diviner, they shall be put to death; for they urged disloyalty to the LORD your God—who freed you from the land of Egypt and who redeemed you from the house of bondage—to make you stray from the path that the LORD your God commanded you to follow. Thus you wil l sweep out evil from your midst.

סַנְהֶדְרִין הַהוֹרֶגֶת אֶחָד בְּשָׁבוּעַ נִקְרֵאת חָבְלָנִית. רַבִּי אֶלְעָזָר בֶּן עֲזַרְיָה אוֹמֵר, אֶחָד לְשִׁבְעִים שָׁנָה. רַבִּי טַרְפוֹן וְרַבִּי עֲקִיבָא אוֹמְרִים, אִלּוּ הָיִינוּ בַסַּנְהֶדְרִין לֹא נֶהֱרַג אָדָם מֵעוֹלָם. רַבָּן שִׁמְעוֹן בֶּן גַּמְלִיאֵל אוֹמֵר, אַף הֵן מַרְבִּין שׁוֹפְכֵי דָמִים בְּיִשְׂרָאֵל:

... A Sanhedrin that would execute somebody once in seven years would be considered destructive. Rabbi Elazar Ben Azariah says: "Once in seventy years." Rabbi Tarfon and Rabbi Akiva said: "If we were on the Sanhedrin , nobody would have ever been executed." Rabban Shim'on Ben Gamliel said: "They too would have increased violence in Israel."

"If the Government has the power to enforce laws in its locale, then its laws are law, for the principle is that the law of the land is law (דינא דמלכותא דינא). THus it is the role of the sovereign government to punish criminals like robbers, thieves, and murderers, and its laws in such matters are law."
Teshuvot of the Rashba, 1.612- Rabbi Shlomo ibn Aderet, 1200s, Spain

ולאפשר רוחב גדול מאד. ואילו התירה התורה לחתוך דיני נפשות באפשר הקרוב מאד שאפשר שיהיה קרוב מן המחוייב המציאות כגון זה שהמשלנו היינו חותכים הגדר במה שהוא רחוק מזה מעט ובמה שהוא יותר רחוק גם כן עד שיחתכו הגדרים וימיתו האנשים פעמים במעט אומד לפי דמיון הדיין ומחשבתו. ולכן סגר יתעלה את הפתח הזה ואמר שלא ייחתך גדר העונש אלא כשיהיו העדים מעידים שהם ידעו בודאי שזה עשה המעשה ההוא באמת בלא ספק ובלא דמיון כלל. וכאשר לא נחתוך הגדרים בדמיון החזק מאד הנה תכלית מה שיהיה שנפטור החוטא וכאשר חתכנו הגדרים בדמיון ובאומד הנה פעמים נהרוג נקי יום אחד. ולזכות אלף חוטאים יותר טוב ונכסף מהרוג זכאי אחד יום אחד.

The realm of the possible is very broad. Had the Torah permitted deciding capital cases based even on a conjecture so likely that it seems absolutely certain, like the example we mentioned [about the person chasing another with a sword], in the next case we would decide based on a conjecture just a little less likely, and in the next, a conjecture less likely still, until we would sometimes execute people based on nothing more than the judge’s imagination and opinion. Thus the Exalted One shut this door, and demanded that we not punish except when witnesses can testify without doubt or conjecture that they are absolutely certain the defendant did this deed. Inevitably, when we do not convict based even on very strong conjecture, we will sometimes acquit the guilty; while when we do convict by conjecture sometimes we will execute the innocent. But it would be better to acquit 1,000 criminals than to kill a single innocent.

Rashba- New Responsa of Rashba, From Manuscript, #345.
The Torah’s procedural rules apply only to the Sanhedrin. But as for the laws of the king, we pay no attention to all that. Royal law is determined exclusively by knowledge of the facts. And therefore one can be executed by royal law based on testimony by relatives or the accused’s confession, without any formal warning, and not by a court of 23 ... If one insists upon following Torah law, as in the process of the Sanhedrin, the world would become desolate, and the murderers and their henchmen would proliferate.

אומר ר"מ משלו משל למה הדבר דומה לשני אחים תאומים בעיר אחת אחד מינוהו מלך ואחד יצא לליסטיות צוה המלך ותלאוהו כל הרואה אותו אומר המלך תלוי צוה המלך והורידוהו:

Rabbi Meir says: The Sages told a parable: To what is this matter comparable? It is comparable to two brothers who were twins and lived in the same city. One was appointed king, while the other went out to engage in banditry. The king commanded that his brother be punished, and they hanged his twin brother for his crimes. Anyone who saw the bandit hanging would say: The king was hanged. The king, therefore, commanded that his brother be taken down, and they took the bandit down.

Kalmanofsky's Teshuva, p.18
If we think Halakhah should defer to military and diplomatic experts about Israel’s security, if we consult scientists and physicians on medical questions, then we should show a similar humility and respect for the secularized, democratic political process on this question.
Kalmanofsky's Teshuva, p.20
This picture that emerges from the unresolved data on deterrence forestalls a univocal halakhic prohibition on the death penalty. Our values might prompt us to conclude that “there is no credible evidence that the death penalty deters crime,” as in a policy statement by the Progressive Jewish Alliance. But such a view is “certainly an exaggeration,” in the view of legal scholar David Garland of NYU, a prominent death penalty expert: “The idea that the death penalty definitely works may be a myth – but this doesn't mean that the opposite is true. Capital punishment is not, as its opponents argue, all costs and no benefits.” Even if no one is ever executed, Garland noted, the threat of death can ease plea bargaining and induce cooperative testimony from conspirators. Garland argues that American capital punishment is part of a cultural, emotional and political discourse around death, but it is not effectively calibrated to control crime: “uncertainty, infrequency and delay undermine its deterrent effect.” America sees more than 16,000 homicides annually, but now issues fewer than 100 new death sentences annually, and has never, in modern times, executed 100 persons in a year. Such numbers would comfortably reassure any rational killer that he will likely escape execution. Only if America’s death penalty were much more sweeping, swift and certain – if it were mandatory without exception, as in Singapore, or employed by the thousands, as in China – would its deterrent effect be maximized, Garland wrote. But certainly Jewish citizens would not want this country to become such a brutal or “bloodthirsty court.”
Kalmanofsky's Teshuva, p.21
Most modern Jewish religious leaders have favored abolition. In Israel, when the young state convicted its first murderer, the two chief rabbis, R. Itzhak Herzog and R. Ben Zion Meir Hai Ouziel, urged the justice minister to nullify the death penalty, left over from the British Mandate; and it was in 1954. R. Aaron Soloveitchik also took this view in a letter to the Orthodox Union in the mid-1970s as that organization was weighing its stance: “It is irresponsible and unfair to submit a statement in favor of capital punishment in the name of Orthodox Jewry. In my humble opinion, from a halakhic point of view, every Jew should be opposed to capital punishment.” R. Moshe Feinstein took a similar view in a responsum he sent on Purim, 1981 to a sar hamedinah, apparently New York Gov. Hugh Carey [Iggerot Moshe HM 2:68].42
Kalmanofsky's Teshuva, p.23
Perhaps a Jewish boycott of the entire capital punishment process would nudge public opinion further toward abolition.
Such conscientious objection might seem at first glance to reflect a good moral intuition, and might seem appealing as a gesture of protest against a repugnant policy. But before coming to that conclusion, a few points bear consideration.
First, although we believe religious Jews should oppose the death penalty on moral and pragmatic grounds, at same time not everything moral by definition imposes a halakhic imperative or a prohibition. Based on all the foregoing, we do not find a halakhic prohibition on participating or a halakhic imperative to refuse to participate in capital cases as witnesses, jurors, prosecutors or judges.
Second, Jewish citizens of the United States are duty-bound to support the state’s fundamentally necessary efforts to restrain criminals and control crime. That duty does not lapse because we object to capital punishment. Do Jewish norms really demand that Jewish Texans, Floridians, Pennsylvanians or Californians (as examples of states with active capital penalties) cede that civic obligation to their gentile neighbors whenever a murder is committed?
Conclusion: How Should Jews Participate in Capital Cases?, p.24-27
In fact, some moral and halakhic factors strengthen the argument for participating in death penalty trials as jurors and judges.
A leading capital defense attorney, Marshall Dayan, argues that it is “tremendously injurious” to defendants when those who object to the death penalty recuse themselves.46 Studies show that such “death qualified” juries – that is, jurors who have asserted during jury selection that they would be willing to impose death penalty – are more likely to convict even for lesser penalties than are juries taken from the general population. Death penalty opponents complain that prosecutors sometimes bluff their way to more congenial juries by saying (disingenuously) that they would seek capital punishment, thus sifting out the most conviction-averse jurors. How would it help vulnerable defendants for Jews, inspired by classical scruples and veneration for human life, to boycott the proceedings, further tilting the odds in favor of the prosecution? In this case, the conscientious refusal to participate in capital trials, which seemed at first glance to be a good moral instinct, turns out to risk harming American justice by leaving these cases only in the hands of those already committed to the death penalty. Instead, it might practically enhance criminal justice for morally scrupulous Jews to serve as judges, prosecutors, jurors and witnesses, to try to mitigate the problems that compromise American capital punishment.47 Such service would not prevent Jews from using other venues to advocate against the death penalty.
Let us consider each of these roles Jewish citizens might play in the criminal process.
Witnesses: This is the least morally freighted of the roles. A witness neither convicts nor acquits and assigns no penalty. A witness merely conveys to the court the information, for judges and jurors to evaluate. Even if that testimony proves decisive, it is not the witness who decided. If one has first-hand, accurate information about a crime, as a matter of public safety, one should speak to the police and testify in court, regardless of one’s moral objection to whatever penalty may ensue. There is no halakhic basis to withhold information from investigators or testimony from court. In fact it would constitute a transgression to fail to give testimony in such a case. “One who is a witness, who sees or knows, but does not testify, will bear his guilt” [Leviticus 5.1]. Withholding testimony might help a violent criminal escape and expose others to future harm. Therefore, according to Maimonides [MT Rotzeah 1.14], withholding testimony violates one of the Torah’s major ethical mandates: “Do not stand idly by the blood of your neighbor” [Leviticus 19.16].
Jurors: In one sense, whether death penalty opponents might refuse to serve on a capital jury is practically a moot question, since prosecutors usually try to identify those with anti-death penalty scruples and exclude them. Yet it can be practical and can accord with halakhic and ethical norms for death penalty opponents to sit on such juries. The Supreme Court has rendered several relevant rulings on this topic. In Witherspoon v. Illinois [1968], the court ruled that jurors cannot be removed for cause simply because they express general ethical or religious reservations about capital punishment. Later rulings in Adams v. Texas [1980] and Lockhart v. Mcree [1986] qualified this view, holding that jurors can be excused or excluded when their views are so strong that they would substantially impair them from performing the duties of the role. But as long as a person can perform a juror’s duty within the law, such a person cannot be stricken for cause. To determine whether they can follow the law, prospective jurors are typically asked something like: Would you always vote for life without the possibility of parole over the death penalty, regardless of the circumstances of the case? Even observant Jews who oppose the death penalty could answer that question in the negative. Let us remember that jury service is part of a citizen’s general duty to fight crime in a society where “the law of the land is the law.” Since, by any honest report, Halakhah recognizes that the death penalty is warranted in extreme cases, there is no halakhic reason why jurors should assert absolutely that they could never impose capital punishment. Observant Jewish jurors could promise to keep an open mind and vote for the death penalty if prosecutors could convince them execution was “the morally appropriate punishment,”49 even if that applied only to a tiny class of cases.
Some might balk at this advice, considering it deceptive, if not an outright lie. I do not agree. In this case, I concur with a recent judgment of Chuck Klosterman, the New York Times Ethicist columnist, who took up this very problem. Prospective jurors should not misrepresent their views, Klosterman said, but should say honestly during jury vetting something like this: “I personally disagree with the state of Missouri’s position on capital punishment, but — if selected — I will perform my duty to the best of my abilities, within the framework of my own conscience.”50
Judges and Prosecutors. The foregoing applies equally and more strongly to prosecutors and judges. Their work helps keep society safe, and so, in its way, is holy work. When the law requires a capital sentence, or when one’s superiors assign one to a capital case, a Jew may fulfill those tasks, albeit reluctantly.
Prosecutors have virtually unfettered discretion over when to seek the death penalty or long-term imprisonment.51 In many jurisdictions, judges are bound to follow juries’ sentencing determinations; in others, judges have discretion to modify those determinations. Jewish values argue that, in the vast majority of cases, except in the greatest exigencies, prosecutors and judges should choose imprisonment over execution. But even in cases where American law dictates a capital punishment, Jewish prosecutors and judges can fulfill their professional duties without transgressing the Torah and the decrees of our Sages.
Prison Guards and Medical Technicians. Presumably the number of Jewish staff working on death rows is negligible. Yet given all that has been said here, we must confront the possibility that a Jewish guard may have to strap a prisoner to a gurney, or a Jewish medical aide may be called upon to administer a lethal injection.52 Such a prospect is genuinely ugly, and we feel a reflex to say that this is no job for a nice Jewish boy or girl. But given everything we have said heretofore, there is no escaping the conclusion that when these employees of the state – like Rabbi Elazar ben Rabbi Shimon, as recorded by the Talmud and Midrash – carry out their duties, they are not murderers, but duly authorized public servants.
Of course, no one has to work in a prison. A person who cannot imagine ending another person’s life should seek another line of work. I can imagine that it would be extremely difficult for a prison employee to end the life of someone that he or she believed was genuinely innocent. In such a case, any prison employee – Jewish or gentile – might wish to petition to be excused from that assignment, without unduly interfering with the implementation of the sentence.
Nonetheless, judicial executions, carried out in accordance with criminal justice laws and proper trials, do not constitute murder, any more than a court-imposed fine constitutes theft. The judges, prosecutors, jurors and witnesses who play their roles in reaching and executing a capital sentence would not be halakhically guilty of causing an unjust homicide.
Ruling
We urge the American federal and state governments to renounce capital punishment except in the rarest cases. Religious Jews should advocate for that position as the superior moral stance and best public policy. But given the weight of precedent, it would be false to assert that Jewish law forbids capital punishment. Halakhah confers on secular governments the legitimate power to punish criminals to protect the innocent, including the right to impose death, when needed, God forbid.
Objection to the death penalty is not halakhic grounds to refuse to participate as judge, prosecutor, juror, police or witness in capital trials.

(ה) כֵּיצַד מְאַיְּמִין אֶת הָעֵדִים עַל עֵדֵי נְפָשׁוֹת, הָיוּ מַכְנִיסִין אוֹתָן וּמְאַיְּמִין עֲלֵיהֶן. שֶׁמָּא תֹאמְרוּ מֵאֹמֶד, וּמִשְּׁמוּעָה, עֵד מִפִּי עֵד וּמִפִּי אָדָם נֶאֱמָן שָׁמַעְנוּ, אוֹ שֶׁמָּא אִי אַתֶּם יוֹדְעִין שֶׁסּוֹפֵנוּ לִבְדֹּק אֶתְכֶם בִּדְרִישָׁה וּבַחֲקִירָה. הֱווּ יוֹדְעִין שֶׁלֹּא כְדִינֵי מָמוֹנוֹת דִּינֵי נְפָשׁוֹת. דִּינֵי מָמוֹנוֹת, אָדָם נוֹתֵן מָמוֹן וּמִתְכַּפֵּר לוֹ. דִּינֵי נְפָשׁוֹת, דָּמוֹ וְדַם זַרְעִיּוֹתָיו תְּלוּיִין בּוֹ עַד סוֹף הָעוֹלָם, שֶׁכֵּן מָצִינוּ בְקַיִן שֶׁהָרַג אֶת אָחִיו, שֶׁנֶּאֱמַר (בראשית ד) דְּמֵי אָחִיךָ צֹעֲקִים, אֵינוֹ אוֹמֵר דַּם אָחִיךָ אֶלָּא דְּמֵי אָחִיךָ, דָּמוֹ וְדַם זַרְעִיּוֹתָיו. דָּבָר אַחֵר, דְּמֵי אָחִיךָ, שֶׁהָיָה דָמוֹ מֻשְׁלָךְ עַל הָעֵצִים וְעַל הָאֲבָנִים. לְפִיכָךְ נִבְרָא אָדָם יְחִידִי, לְלַמֶּדְךָ, שֶׁכָּל הַמְאַבֵּד נֶפֶשׁ אַחַת מִיִּשְׂרָאֵל, מַעֲלֶה עָלָיו הַכָּתוּב כְּאִלּוּ אִבֵּד עוֹלָם מָלֵא. וְכָל הַמְקַיֵּם נֶפֶשׁ אַחַת מִיִּשְׂרָאֵל, מַעֲלֶה עָלָיו הַכָּתוּב כְּאִלּוּ קִיֵּם עוֹלָם מָלֵא. וּמִפְּנֵי שְׁלוֹם הַבְּרִיּוֹת, שֶׁלֹּא יֹאמַר אָדָם לַחֲבֵרוֹ אַבָּא גָדוֹל מֵאָבִיךָ. וְשֶׁלֹּא יְהוּ מִינִין אוֹמְרִים, הַרְבֵּה רָשֻׁיּוֹת בַּשָּׁמָיִם. וּלְהַגִּיד גְּדֻלָּתוֹ שֶׁל הַקָּדוֹשׁ בָּרוּךְ הוּא, שֶׁאָדָם טוֹבֵעַ כַּמָּה מַטְבְּעוֹת בְּחוֹתָם אֶחָד וְכֻלָּן דּוֹמִין זֶה לָזֶה, וּמֶלֶךְ מַלְכֵי הַמְּלָכִים הַקָּדוֹשׁ בָּרוּךְ הוּא טָבַע כָּל אָדָם בְּחוֹתָמוֹ שֶׁל אָדָם הָרִאשׁוֹן וְאֵין אֶחָד מֵהֶן דּוֹמֶה לַחֲבֵרוֹ. לְפִיכָךְ כָּל אֶחָד וְאֶחָד חַיָּב לוֹמַר, בִּשְׁבִילִי נִבְרָא הָעוֹלָם. וְשֶׁמָּא תֹאמְרוּ מַה לָּנוּ וְלַצָּרָה הַזֹּאת, וַהֲלֹא כְבָר נֶאֱמַר (ויקרא ה) וְהוּא עֵד אוֹ רָאָה אוֹ יָדָע אִם לוֹא יַגִּיד וְגוֹ'. וְשֶׁמָּא תֹאמְרוּ מַה לָּנוּ לָחוּב בְּדָמוֹ שֶׁל זֶה, וַהֲלֹא כְבָר נֶאֱמַר (משלי יא) וּבַאֲבֹד רְשָׁעִים רִנָּה:

(5) How do we press the witnesses in a capital case? We bring them in [to the court's chambers] and press them: "Perhaps what you say [isn't eyewitness testimony] is but your own assessment, or from rumors, or your witnessing an actual witness testify, or your reporting what a trustworthy said. Or perhaps you were unaware that by the end we'd interrogate you, with examination and inquiry. Know that capital cases are not like monetary ones. In monetary cases, [a false witness] can return the money and achieve atonement. But in capital cases, the blood of [the victim [and all his future offspring hang upon you until the end of time. For thus we find in regard to Cain, who killed his brother, "The bloods of your brother scream out!" (Genesis 4:10) - the verse does not say blood of your brother, but bloods of your brother, because it was his blood and also the blood of his future offspring [screaming out]! [Another explanation of the verse: for his blood was splattered over the trees and rocks [there was more than one pool of blood]. [The judges' speech continues] "It was for this reason that man was first created as one person [Adam], to teach you that anyone who destroys a life is considered by Scripture to have destroyed an entire world; and anyone who saves a life is as if he saved an entire world." And also, to promote peace among the creations, that no man would say to his friend, "My ancestors are greater than yours." And also, so that heretics will not say, "there are many rulers up in Heaven." And also, to express the grandeur of The Holy One [blessed be He]: For a man strikes many coins from the same die, and all the coins are alike. But the King, the King of Kings, The Holy One [blessed be He] strikes every man from the die of the First Man, and yet no man is quite like his friend. Therefore, every person must say, “For my sake ‎the world was created.”‎ [The judges' speech continues:] "Maybe you [the witnesses] will now say, 'What do we need this, and all this anxiety for [let's not come forward even with true testimony]!' But Scripture has already spoken: "If he be a witness - having seen or known - if he does not express it, he shall bear his sin." (Lev. 5:1) Maybe you will now say, 'What do we need this, to be responsible for another man's death?' But Scripture has already spoken: "When the wicked are destroyed there is rejoicing." (Prov. 11:10)"