N.H. Rev. Stat. Ann. § 659:20-a

Any voter, after appearing at the polling place location prior to the closing of the polls to vote in person, who declares to the moderator under oath that said voter is unable to access a polling place due to disability shall, upon the voter's request, have the required documents delivered to the voter outside the guardrail by the town or ward clerk or one of his or her assistants. The absentee ballot delivered by the town or ward clerk shall be processed using the same procedures as any other absentee ballot except that the cutoff time listed in RSA 657:22 shall not apply.