N.H. Rev. Stat. § 657:13
Upon receipt of a properly executed application for an official absentee ballot for a state or presidential primary election, whether the form supplied by the secretary of state or a written statement containing the information required by RSA 657:4, I, a town or city clerk shall forthwith ascertain if the person is on the checklist of the town or city and is properly registered as to party designation. If such person is found to be on the checklist and to be properly registered or if such person is found to be on the checklist but is not registered as a member of any party, but the information supplied states he or she is applying for a ballot of a political party, the person shall be registered as a member of said party; and, in either case, the clerk shall send the materials provided for in RSA 657:15. If the person is not on the checklist or is registered as a member of a party different from the one whose ballot he or she is applying for, the clerk shall refuse to certify as provided in RSA 657:16. An application may be transmitted by facsimile to a town or city clerk.
RSA 657:13
1979, 436:1. 2003, 8:2. 2010, 182:3, eff. June 21, 2010; 317:27, eff. July 18, 2010.