When county moneys have been deposited in any such depository they shall be withdrawn therefrom only in the following manner: Funds designated in Section 3-11003 as “Class A” funds and as “Class B” funds shall be withdrawn only upon checks or drafts signed by the County Treasurer and payable to the order of the State Treasurer or the other proper authorities or persons entitled by law to receive the same; funds designated in said Section 3-11003 as “Class C” funds shall be withdrawn only upon checks or drafts signed by the county treasurer and supported by warrants signed by the County Clerk and countersigned by the president or chairman of the county board; funds designated in said Section 3-11003 as “Class D” funds shall be withdrawn only upon checks or drafts signed by the County Treasurer and payable to persons entitled to receive the same; Provided, however, that subject to the limitations hereinafter set forth in Section 3-11011, the County Treasurer shall have the power to withdraw such county moneys from any depository in the cases provided for and under the circumstances stated in Sections 3-11009 and 3-11010, and, provided further, that the provisions of this Division regarding the proper payees of checks or drafts shall not be construed to obligate any depository to investigate or determine the right of any payee to receive payment or any check or draft of the County Treasurer.