The board of supervisors shall thereupon levy upon the taxable property of the district within its own county a tax sufficient in amount to maintain the district but not to exceed the twenty-cent ($0.20) limit provided in Section 32203 and, in addition, a tax sufficient to pay the interest on all outstanding bonds of said district as the same becomes due, and also to constitute a sinking fund for the payment of the principal thereof at maturity, and a tax sufficient to pay rentals and all other sums due or payable under any agreement for the construction and leasing or purchasing of any hospital buildings or facilities entered into by the district pursuant to Section 32135 prior to January 1, 1959. If the district embraces territory lying in more than one county, the amount estimated shall be ratably apportioned among the several counties in the district in proportion to the assessed value of the property in the several counties included within said district as shown upon the last assessment rolls of the said counties, and the estimates apportioned to the several counties shall be rendered to their respective boards of supervisors and the tax shall be levied and collected by the officials of each county upon the property of the district lying therein.