N.H. Rev. Stat. § 660:11
The secretary of state shall request that all town and city clerks forward ballots containing such proposed amendment to the secretary of state forthwith, and the clerks shall immediately forward them. At the time and place so appointed, the ballots shall be counted by the secretary of state and such assistants as the secretary of state may require. 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 ballots shall be open to the inspection of the petitioners and other interested persons under such suitable rules as the secretary of state may prescribe. 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 660:11
1979, 436:1. 2006, 41:2, eff. June 17, 2006.