The salaries of all City officials and employees, the payrolls of all public boards, corporations or authorities, the public money of which is deposited by the Treasurer, pursuant to the terms of this chapter or the laws of this State, may be paid in cash. To provide money for such payment the Commissioner of Accounts shall issue his or her warrant authorizing the issuance of checks upon the depositary for such amount stated in the warrant, as shall be sufficient to meet such demands. All other warrants shall be drawn in favor of the persons to whom the amounts specified therein respectively are due, or in favor of their assigns.