N.H. Rev. Stat. Ann. § 40:4-d

If, in the case of a recount of votes, it shall appear that the result of the vote on the question was other than as declared by the moderator, the board of recount shall declare the result found by it and shall, after 5 days from such declaration, if no appeal is taken to the superior court, certify such declaration to the town clerk and said declaration shall be final, unless the result is changed upon appeal to the superior court.