N.H. Rev. Stat. Ann. § 670:4

To become a candidate for any village district office, a person must have a domicile in the village district. In any village district which has voted to elect district officers by non-partisan official ballot as provided in RSA 669:13, all candidates shall file a declaration of candidacy with the village district clerk, in the same manner as with the town clerk in town elections as provided in RSA 669:19-669:22.