Mo. Rev. Stat. § 182.170: Trustees, number, appointment.

When any city establishes and maintains a public library under sections 182.140 to 182.301, the mayor or other proper official of the city, with the approval of the legislative branch of the city government, shall proceed to appoint a library board of nine trustees, chosen from the citizens at large, with reference to their fitness for the office. No member of the city government shall be a member of the board.