The appointing authority may dismiss, issue non-punitive disciplinary letters to, or demote any nurse in the classified service provided the rules and regulations of the Civil Service Commission are followed. If they do not appeal such action to the Civil Service Commission within fourteen (14) days after receipt of such charges, as provided in the Charter, a permanent nurse shall have the right to appeal such action in accordance with the provisions of Section 35.2 (c) and (d) unless their objection to the action has been resolved earlier in accordance with Section 35.2 (a) or (b).