N.H. Rev. Stat. Ann. § 657:23

Upon election day, prior to the closing of the polls or the time set for processing absentee ballots in accordance with RSA 659:49, the clerk shall deliver all such envelopes, the applications therefor received by him or her, and the list of absentee voter applicants compiled pursuant to RSA 657:15 to the moderators in the several voting precincts in which the absentee voters assert the right to vote, taking a receipt from the moderator thereof; except that no UOCAVA voter's ballot shall be rejected by a moderator for lack of an attached application, provided a signature is available for comparison on a voter registration document.