N.H. Rev. Stat. Ann. § 31:23

A town wherein the total book value of trust funds is less than $15,000, acting under an appropriate article in the warrant for any annual town meeting, may vote that the board shall consist of one trustee only, in which case said trustee shall be chosen by ballot at the same and each succeeding annual town meeting; and such vote may be rescinded in like manner. All the duties and obligations imposed by law upon a board of trustees shall devolve upon the trustee so chosen; vacancies shall be filled by the selectmen for the remainder of the year; and said trustee shall receive from the town treasury such compensation as the town meeting may determine.