Tenn. Code § 40-25-139
The state shall pay and refund to any county of the state any moneys that have been irregularly or otherwise paid, or that shall be irregularly or otherwise paid in connection with criminal prosecutions, by any county of the state, which should have been paid by the state, if the same had been adjudged, authenticated and presented for payment as provided by law, or any moneys that have been, or shall be paid, by any county to the state, to which the state is not entitled, or shall not be entitled in connection with criminal prosecution. If bills or claims for the moneys have been filed in the office of the commissioner of finance and administration, or shall be filed in the office of the commissioner of finance and administration, sworn to by the county mayor of the county, the comptroller of the treasury shall immediately have the claim or claims audited, and when the audit has been completed, the commissioner will draw a warrant or warrants on the state treasurer, in favor of the county, for so much and the parts of the claim or claims as shall be found correct by the auditors auditing the same, which warrants shall be payable out of the miscellaneous funds of the state treasury. No claim for moneys paid by the county on behalf of the state may be allowed where the claim is filed with the comptroller of the treasury more than six (6) years after the date of the payment by the county.
T.C.A. § 40-25-139