Kan. Stat. § 14-604
A hospital having been established, the governing body shall proceed at once to appoint three trustees, chosen from the citizens of the city with reference to their fitness for such office, who shall constitute a board of trustees for said hospital. The said trustees shall hold their offices until the next following city election, when three trustees shall be elected and hold their offices, one for one year, one for two years and one for three years. At each subsequent city election, the trustee whose term is about to expire shall be filled by the nomination and election of hospital trustee in the same manner as other officers are elected, none of whom shall be physicians. In any city in which a regular city election as provided by law may be held only once every two years, then there shall be elected one trustee for a two-year term of office and one trustee for a four-year term of office or until their successors shall have been respectively elected and qualified, and the person receiving the greater number of votes shall be deemed elected to the four-year term of office. Any trustee now holding office whose term will expire in an even-numbered year shall hold over and continue in office until a successor shall be duly elected and qualified as provided herein.
Notwithstanding the foregoing provisions to the contrary, from and after the effective date of this act the governing body by resolution may increase the number of trustees to serve on the board to five (5) or seven (7) members. In the event the governing body does not increase by resolution the number of members to serve on the board of trustees, said board of trustees shall consist of three (3) members. Whenever the number of members of an existing board of trustees is increased by resolution of the governing body, said governing body shall provide by resolution for the initial appointment or election of the new members. The governing body shall also provide by resolution for the expiration of the terms of the members initially appointed or elected to new positions on the board of trustees.
K.S.A. 14-604