Sums necessary for the establishment and operation of regional libraries shall be provided by the boards of supervisors of each of the counties included in such region by an appropriation from the general fund of the respective counties, or by a tax levy for this purpose authorized by a vote of the qualified electors in each of the counties. A budget shall be proposed annually by the board of trustees of the regional library to the boards of supervisors of the counties in the region. Upon approval of such budget by a majority of each of said boards of supervisors, the proposed budget shall be effective in all counties in the region. All appropriations shall be paid to the board of trustees and disbursed under its direction by the county treasurer of the county designated by the regional library board as depository for the regional library fund.