N.H. Rev. Stat. Ann. § 652:13

"Federal election" shall mean any state general, special, or primary election held solely or in part for the purpose of choosing or nominating any candidates for the offices of president, vice-president, United States senator, or United States representative. For federal ballot only voters domiciled outside the United States who are eligible to vote in federal elections as provided in RSA 657:2, "federal election" shall also include any presidential primary election.