N.H. Rev. Stat. Ann. § 656:35

Absent uniformed services voters and voters temporarily residing outside the United States shall be provided with the absentee ballot prepared under RSA 656:33, provided that the secretary of state shall prepare an electronic version of such ballot for use by any absent uniformed services voter or voter temporarily residing outside the United States who requests that his or her absentee ballot be transmitted to the voter electronically pursuant to RSA 657:19.