(a) At least thirty days prior to each regular session of the Legislature, the board of trustees shall certify to the Governor the contributions, determined according to section thirty-one hereof, to be made by the state to the retirement system for the next following fiscal year; the said contributions to be based upon the state's total payroll for the preceding twelve calendar months. The amounts so ascertained shall be included in the appropriation bill to be submitted to the Legislature. In the event the state's contributions for the fiscal year are less than they would have been based upon the state's actual payroll for the fiscal year, the amount of the insufficiency shall be included in the appropriation bill for the next following fiscal year. The said contributions shall be paid to the retirement system quarterly and when paid shall be credited to the employers accumulation fund.
(b) In the case of any member whose compensation is paid out of moneys derived in whole or in part out of any special fund, or from any source other than the state, then contributions on behalf of such member in any year shall be paid out of such special fund or by such other source in proportion to that part of the member's compensation derived therefrom for that year. The governing body of each participating public employer is hereby authorized to make such contributions from funds of the participating public employer as shall be necessary to pay its proportionate share of contributions on account of each state employee whose compensation is paid by such participating public employer.