N.H. Rev. Stat. Ann. § 658:5

In making appointments of inspectors of elections as provided in RSA 658:2, political committees or, in the absence of such appointments by a political committee, the town and ward selectmen, in consultation with the moderator, may designate a list of alternates to the list of appointed inspectors, who shall meet the same qualifications as inspectors of elections. Alternates shall be called in numerical order to serve in case one or more of the principal appointees fails to accept the appointment or is otherwise unavailable to perform his or her duties.