N.H. Rev. Stat. Ann. § 659:55

Notwithstanding any other provision of law, if a red ink "A.V." is properly placed against the name of a voter who has voted by absentee ballot, that voter against whose name the red ink "A.V." has been properly placed and who has voted by absentee ballot shall not be permitted to vote in person. The ballot clerk shall notify the moderator if a voter appears at the polling place on election day to vote and that voter's name has been marked as voting absentee on the checklist.