(1) The chief of each department may at any time suspend any subordinate officers, members, employees, or agents employed therein when in his judgment the good of the service demands it, and during the time of suspension, the person suspended is not entitled to any salary or compensation whatsoever.
(2) Any suspension of employees in the classified civil service which exceeds three days or 24 working hours is subject to an appeal to the civil service commission as provided in Section 10-3-1012.