(a) The board shall select one or more depositories for the district in the manner provided by law for the selection of a county depository.
(b) A depository selected by the board shall be the depository of the district until one or more successors are selected and qualified.

(c) All income received by the district, including tax revenue after deducting discounts and fees for assessing and collecting the taxes, shall be deposited with the hospital depository and may be withdrawn only as provided by this chapter.