N.H. Rev. Stat. Ann. § 202-A:8

The trustees of a public library in a city shall be elected as provided in the city charter. In case of trustees of a city library acquired by a city in whole or in part, by donation or bequest containing other conditions or provisions for the election or appointment of trustees, which conditions do not provide for a representative of the public on the board, the city council shall elect to said board a public trustee for a 3-year term.