N.H. Rev. Stat. § 660:13
Five legal voters of any city or town which has voted on any question other than constitutional amendments printed on the ballot at any state election as provided in RSA 663 may, no later than the second Friday after the election, petition the secretary of state for a recount of the votes cast upon said questions. Such application shall be accompanied by a fee of $10 for each 1,000 ballots or fraction thereof cast at the election in said town; however, in no event, shall the fee exceed $50. The secretary of state shall fix a time for recount and shall notify the petitioners and the selectmen, clerk and moderator of the town or the mayor and clerk of the city of the time and place so fixed. He shall request the clerk having custody of the ballots to forward them forthwith to the secretary of state, and the clerk shall immediately forward them.
RSA 660:13
1979, 436:1. 1994, 4:25, eff. May 27, 1994.