On or before August 1st the board of any district which has elected pursuant to Section 37203 to proceed under this part shall furnish to the county auditor and the board of supervisors an estimate in writing of the amount of money needed to be raised by assessment in the county for the payment of its proportion of the amount required for the purposes of the district for the next fiscal year. Except to the extent that provision has otherwise been made by the board, as may be permitted by law, for payment of the principal of and interest upon bonds as they become due and for payment of other claims and expenses of the district, said estimate shall be in an amount sufficient for payment of the county’s proportion of the principal of and interest on bonds as they become due and for payment of other claims and expenses of the district.