N.H. Rev. Stat. Ann. § 671:18

To become a candidate for any school district office, a person must be a registered voter in the district. No person holding the office of member of the school board shall at the same time hold the office of district moderator, treasurer, or auditor. No person employed on a salaried basis by a school administrative unit or by any school district within a school administrative unit shall be a school board member in any district of the school administrative unit. Salaried positions shall include, but are not limited to, the following: teacher, custodian, administrator, secretary, school bus driver (if paid by the district), school lunch worker and teacher's aide.