N.H. Rev. Stat. Ann. § 657:22

In any state election, a town or city clerk shall not accept any completed absentee ballots delivered to the clerk after 5:00 p.m. on election day except as provided in RSA 657:21-a, V and RSA 659:20-a. The clerk shall record absentee ballots received after such time in the statewide centralized voter registration database with the return date and shall mark the ballot as rejected due to absentee ballot receipt after election day. The clerk shall retain the unopened ballot until the time set for the destruction of other state election ballots as provided in RSA 659:100 at which time the envelopes shall likewise be destroyed, unopened and unexamined.