N.H. Rev. Stat. Ann. § 657:12

Upon receipt of a properly executed application for an official absentee ballot for a general election, whether the form supplied by the secretary of state, the federal official post card form, or a written statement containing the information required by RSA 657:4, I, a town or city clerk shall forthwith ascertain if the applicant is on the checklist of the town or city. If the applicant is on the checklist, the clerk shall send the materials provided for in RSA 657:15 to the applicant and record the information pursuant to RSA 657:15; if not, 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.