Tennessee Code Title 40. Criminal Procedure § 40-25-137

(a) A copy of the judgment and bill of costs, certified by the clerk of the court, as provided in § 40-25-136, shall be presented to the director of accounts, or county mayor, as the case may be, who, after the bills have been examined and approved by the clerk of the court, is granted full power, and it is the director's or county mayor's duty, to examine into, inspect and audit all bills of costs accruing against the state or county; and disallow any part of the bills of costs that may be illegally or wrongfully taxed against the state or county. The commissioner of finance and administration or county mayor may disallow any and all costs taxed against the state or county on account of malicious, frivolous or unnecessary prosecution, in the event the clerk of the court should, by mistake or otherwise, approve any of the bills.

(b) After correcting and auditing the bills of costs, the commissioner, or county mayor as the case may be, shall issue a warrant for the amount, which shall be paid to the clerk or any other person authorized by the clerk, in writing, to receive the funds.