N.H. Rev. Stat. Ann. § 97:1

Each county, town, city, precinct, school board or other political subdivision of the state shall reemploy a veteran of any branch of the military service of the United States who has been placed on inactive status or been given a discharge other than dishonorable and who, within 90 days after being so made inactive or discharged, in writing, notifies the treasurer or other fiscal agent of such political subdivision that he desires to be reinstated in the position he held with such political subdivision at the time he entered said military service.