Mo. Rev. Stat. § 182.050
For the purpose of carrying into effect sections 182.010 to 182.120, in case a county library district is established and a free county library authorized as provided in section 182.010, within sixty days after the establishment of the county library district, there shall be created a county library board of trustees, of five members, who shall be residents of the library district, none of whom shall be elected county officials. The members shall be appointed by the county commission for terms of four years each, except that as to the members of the first board, two shall be appointed for one year, and one each shall be appointed for two years, three years, and four years, respectively, from the first day of July following their appointment; and annually thereafter before the first day of July the county commission shall appoint successors. Vacancies in the board occasioned by removals, resignations or otherwise shall be reported to the county commission and shall be filled in like manner as original appointments; except that if the vacancy is in an unexpired term, the appointment shall be made for only the unexpired portion of that term. No member of the board shall receive compensation as such. No person shall be employed by the board of library trustees or by the librarian who is related within the third degree by blood or by marriage to any trustee of the board.
§ 182.050, RSMo