(a) A county depository shall pay a check or order for payment drawn by the county treasurer against funds deposited with the depository on presentation of the check or order if the funds subject to the check or order are in the possession of the depository, and, in the case of a time deposit, if the agreed period of notice has expired.
(b) If the commissioners court selects a depository in another county, the depository shall file a statement with the county treasurer designating the place in the county governed by the commissioners court where, and the person by whom, deposits by the treasurer may be received and checks will be paid, or the place in another county where deposits may be made and checks may be paid. The statement must be filed within five days after the date notice is given to the depository of its selection.

(c) An order for payment or check, including an order or check issued prior to September 1, 1993, issued by the county treasurer in settlement of a claim against a county that is not presented for payment before the 366th day following the date of issuance is overdue and nonnegotiable. The sum of the overdue order or check shall be credited as revenue to the county if delivery to the payees was attempted or occurred within a reasonable time following the issuance of the order or check. No right to full settlement of a proper unpaid claim is extinguished by this subsection.