A classified employee with temporary status may be dismissed at the pleasure of an appointing authority under the provisions of § 36-4-31. A classified employee with provisional or probationary status may be dismissed for reasons relating to the employee’s qualifications or for the good of the service. A classified employee with permanent status may be dismissed by an appointing authority whenever he or she considers the good of the service to be served thereby, stated in writing, with full and sufficient reason, and filed with the personnel administrator. Any removal or separation of an employee from the classified service not otherwise provided for in this chapter shall be deemed to be a dismissal. In every case of dismissal, the appointing authority shall on or before the effective date thereof give written notice of this action and the reason therefor to the employee and shall file a copy of the notice with the personnel administrator not later than three (3) days after the effective date.