N.H. Rev. Stat. Ann. § 202-A:7

In any town where a public library has been acquired by the town, in whole or in part, by donation or bequest containing other conditions or provisions for the election of its trustees or other governing board, which conditions have been agreed to by vote of the town and which conditions do not provide for a representative of the public, a special library trustee, to represent the public, shall be elected by the town for a 3-year term. Said special trustee shall act with the other trustees.