Section 44H. The regional refuse disposal district committee shall annually determine the amounts necessary to be raised to maintain and operate the district during the ensuing fiscal year, and the amounts required for payment of debt and interest incurred by the district which will be due in the said year, and shall apportion the amount so determined among the several member cities and towns in accordance with the terms of the agreement. The amounts so apportioned for each city or town shall, prior to December thirty-first in each year, be certified by the regional district treasurer to the treasurers of the several cities and towns. The obligation of each member city or town to pay apportionments pursuant to the agreement shall be included in the amounts to be assessed annually in such city or town under section twenty-three of chapter fifty-nine without appropriation and the city or town treasurer shall pay to the district the amounts so apportioned at the times specified in the agreement. The amounts apportioned or to be apportioned pursuant to the agreement shall not be included in the statutory limit of indebtedness of any city or town.