(a)  All persons in the service of the state on and after July 1, 1960, whether elected, appointed or employed, who elect to participate in an insurance contract or contracts shall be eligible to participate therein. The director, however, with the consent of the insurance company or companies, may by rule or regulation exclude those classes of temporary, part-time, or intermittent employees for whom insurance contracts shall be deemed to be impracticable.

(b)  The director, with the consent of the insurance company or companies, may authorize the inclusion in insurance contracts of employees of public authorities, full-time employees of organizations representing state employees, or other appropriate agencies of the state as may be designated in the rules or regulations of the director, and may prescribe the rate of contribution required from such participating authorities, or other agencies.