N.H. Rev. Stat. § 660:12
The secretary of state shall recount the ballots cast on any question which may be submitted to the voters of a county at a state general election under the provisions hereinafter set forth. Application for such recount shall be by written petition signed by at least 50 legal voters of said county presented to the secretary of state no later than the second Friday following the state general election. The recount shall take place at any suitable state facility in the city of Concord as may be designated by the secretary of state at such time as the secretary of state may appoint and under such rules of procedure as he or she shall determine. When counting the ballots, the secretary of state or his or her assistants shall visually inspect each ballot. No mechanical, optical, or electronic device shall be used for the counting of ballots. The secretary of state shall publish notice of the time and place of the recount once in a paper of general circulation throughout the county. The fee for such a recount on a question voted on throughout a county shall be $25 which shall be paid to the secretary of state by the person submitting the application. If, after the recount, it shall appear that the result of the voting on said question is other than that declared upon the original canvass of votes, the secretary of state shall declare the result found upon recount which shall be final unless the result is changed as a result of an appeal taken to the superior court.
RSA 660:12
1979, 436:1. 1994, 4:24. 2006, 41:3, eff. June 17, 2006.