After a federal jury voted unanimously last week to sentence Gary Lee Sampson to death for his 2001 murder spree, his lawyers want to know whether a mysterious letter one juror tucked into the envelope carrying the verdict slip had anything to do with the decision.

Days after the verdict was announced last Monday, lawyers for the admitted killer asked a judge to release the letter, which was written by one of the jurors, who slipped it into the envelope without it being seen by any of the others.

The lawyers suggested in court filings that the letter could reveal whether there were any improprieties during the jury deliberations, including possible coercion by other jurors.

“That a juror had attempted to put [the letter] into the packet apparently without the knowledge of the others suggested that at least one juror felt a need to communicate outside the channel of the foreperson, raising the possibility that the legally relevant findings of all the jurors might not be adequately represented by the verdict form,’’ the lawyers argued in a court motion Wednesday asking for the release of the letter.

Prosecutors did not immediately respond to the request, though they opposed the release of the letter when it was first disclosed by the jurors, before the verdict was announced.

The motion offers a foreshadowing of the litigation that will undoubtedly persist in Sampson’s case long after Monday’s verdict, the second time a jury agreed to sentence him to death.

In 2003, a federal jury handed Sampson a death sentence for the killings of 19-year-old Jonathan Rizzo, a college student from Kingston, and Philip McCloskey, a 69-year-old retired plumber from Taunton, but a judge vacated that verdict after finding that one of the jurors had lied during screening.

Federal prosecutors sought capital punishment in a retrial, and a new jury agreed last Monday to sentence Sampson to death for the killing of Rizzo. The jury could not come to a unanimous agreement on a sentence for the killing of McCloskey, and so Sampson will get a sentence of life in prison without the possibility of parole for that crime.

The jurors have not been publicly identified and could not be reached for comment.

US District Judge Leo T. Sorokin scheduled a sentencing hearing for Feb. 3. The jury determines the sentence, but only a judge can hand out punishment, though Sorokin is bound by the jury’s decision.

Lawyers for Sampson have asked him to postpone the sentencing hearing, pending a request to dismiss the verdict and pending a mental competency exam for Sampson that was started at the beginning of the trial, which lasted two months.

The judge had proceeded with the trial pending results of the competency exam. But Sampson’s lawyers said he was not capable of assisting them in preparations, and the trial concluded before the exam report was completed.

The case will also undergo a lengthy automatic appeal once the sentence is imposed.

Without reading the letter, Sorokin sealed it as part of the record at the request of defense lawyers. Sampson’s lawyers’ quick focus on the jury letter, which Sorokin refused to release before the jury verdict was announced, could indicate it will be part of that appeal. The jury forewoman had sent a question to the judge Monday alerting him to the letter.

She said a juror was checking signatures on a signed verdict form — before it was delivered to the judge — and noticed the letter tucked between the form’s pages.

Michael Burt, one of Sampson’s lawyers, asked to see the letter at that time, wondering whether one of the jurors could be complaining of coercion toward a vote for the death penalty, which must be unanimous.

But Assistant US Attorney Zachary Hafer opposed the request, saying the lawyers should not speculate on the the letter’s contents, saying the message could be as mundane as a complaint about the defense team presentation.

Sorokin agreed and reinstructed the jury that the forewoman should moderate the deliberations and that any questions should be sent officially to the judge. The jury’s final say would be relayed solely through the verdict form, he told jurors.

Minutes later, the jury sent a letter back confirming that it reached a unanimous verdict.

The lawyers argued that the letter should be released so that any questions “which have the potential to undermine confidence in the reliability of this outcome, may be put to rest.’’

Milton J. Valencia can be reached at milton.valencia-@globe.com. Follow him on Twitter @miltonvalencia.