N.H. Rev. Stat. Ann. § 45:1

The qualified voters in each ward, at the meeting for the choice of city and ward officers, shall give in to the moderator their votes for a mayor of the city, which shall be received, sorted, counted and declared, and a record thereof made in the same manner as votes for senators; and a copy of the record, certified by the moderator, a majority of the selectmen and the ward clerk, shall be delivered by the ward clerk to the city clerk within 24 hours after the meeting.