The governing body of any such city is hereby vested with the authority to manage and control such hospital and it may lease, let or rent to any person, persons, corporation, or other legally organized society, the buildings herein provided for upon such terms and conditions, including special rates for water, light and power, as it may by resolution declare, or it may appoint six (6) trustees chosen from the citizens of said city with reference to their fitness for such office, who together with the mayor, as ex officio member, shall constitute a board of trustees for said hospital. The board of trustees shall hold their offices until the next following city election, when six (6) trustees shall be elected, and hold their offices, two (2) for one (1) year, two (2) for two (2) years, and two (2) for three (3) years. At each subsequent city election, the office of each trustee whose term is about to expire shall be filled by the nomination and election of hospital trustees in the same manner as other officers are elected, none of whom shall be a physician: Provided, That if a board of trustees is appointed or elected, no contract for the leasing, letting or rental of said hospital or buildings shall be made unless and until the terms and provisions thereof shall have been approved by the board of trustees: Provided further, That if a board of trustees is appointed, or elected, the government of such hospital shall be as provided for in Kan. Stat. Ann. §§ 14-605 to 14-614, inclusive, or any amendments thereto.