Mo. Rev. Stat. § 205.470
When any such township or townships shall decide to establish and maintain a hospital under the provisions of sections 205.460 to 205.570, the county commission of such county of which said township or townships is a part shall appoint a board of six trustees for the same, chosen from the voters of such township or townships. Such trustees shall serve without compensation. Such trustees appointed under the provisions of sections 205.460 to 205.570 shall hold office respectively for the term of two and four years as indicated and fixed in the order of the county commission appointing them. Every two years thereafter three trustees shall be elected at the municipal election who shall hold their office for the term of four years and until their successors are elected.
§ 205.470, RSMo