The provisions of Sections 36-26-60 through 36-26-63 shall apply to all officers and employees in the service of the state institutions except:
(1) Members of appointive boards and commissions;
(2) Physicians, surgeons, dentists, psychologists, social workers, nurses and attorneys;
(3) Any person whose employment is subject to the approval of the United States government, or any agency thereof;
(4) Heads of departments in the state institutions; and
(5) Such custodial and laboring positions as may be designated by the State Personnel Department.