N.H. Rev. Stat. Ann. § 654:13-a

All voter registration forms and other records relating to voter registration shall be retained securely in a municipal office under the direction of the town or city clerk. Those forms and records shall be readily accessible to the supervisors of the checklist. Any voter registration document submitted at a meeting of the supervisors of the checklist or at the polling place shall be filed at the office of the town or city clerk within 10 days of the meeting or election at which it was submitted.