N.H. Rev. Stat. Ann. § 44:5

Any person having his or her domicile within the city, qualified to vote as provided in RSA 654:1 through 654:6 and whose name is on the checklist shall be qualified to vote in city elections. The supervisors of the checklist shall prepare, post, and revise the checklist for city elections in the same manner as for a state election as provided in RSA 654:25-654:31.