N.H. Rev. Stat. Ann. § 669:65

Vacancies in the office of town clerk shall be filled by appointment made by the selectmen except in towns in which pursuant to RSA 41:18 the selectmen have previously appointed a deputy town clerk, in which case the deputy shall serve as town clerk until the next annual town election, unless the deputy does not have his or her domicile in the town, in which case the vacancy shall be filled by appointment made by the selectmen.