(a) In any city establishing or continuing a civil service system pursuant to the provisions of this chapter, the city council or other governing body of the city shall name by ordinance five (5) citizens of the city as a civil service commission for the system.
(b) The members of the commission shall hold office as follows:
(1) One shall hold office until the first Monday in April of the second year after his or her appointment;
(2) One shall hold office until the first Monday in April on the fourth year after his or her appointment;
(3) One shall hold office until the first Monday in April of the sixth year after his or her appointment;
(4) One shall hold office until the first Monday in April of the eighth year after his or her appointment; and
(5) One shall hold office until the first Monday in April of the tenth year after his or her appointment.
(c) If any city establishing or continuing a civil service system under this chapter already has a five-member commission for uniformed employees, the existing commission shall also be the commission for the system established or continued under this chapter.