The legislative body may maintain its own pension and retirement fund or may contract with the legislative body of any city or county in the State, or any state department, for:
(a) The performance of any service in connection with the establishment or administration of the retirement system.
(b) The investment, care, or administration of retirement funds.
(c) Any other service relating to the system or its funds.
(Added by Stats. 1949, Ch. 79.)