N.H. Rev. Stat. Ann. § 194:35

No high school shall be discontinued, or the location thereof be changed, except by the superior court, on petition of 20 or more legal voters of the town or district in which such high school is located, in addition to a majority of the school board for said town or district, after such notice as the court may order and proof that the educational interests of the town or district require such discontinuance or change.