(a) All persons who become state employees as defined in this article and who are eligible as specified in the rules and regulations of the board shall become members of this health insurance program unless the employee rejects or waives such coverage in writing.

(b) Any annuitant or person appointed to an emeritus position or any person eligible to be covered by the medical care for the aged program of the Social Security Administration, which person is included in the coverage of any health insurance plan established as provided in this article, may withdraw from such plan and discontinue his coverage thereunder in such manner as may be provided by rules and regulations promulgated and adopted by the board. In the event any such annuitant or person appointed to an emeritus position withdraws from such plan and discontinues his coverage thereunder, coverage of his spouse and dependent child or children shall likewise be withdrawn and coverage thereunder discontinued.