Tenn. Code Ann. § 40-25-142

The costs in §§ 40-25-140 and 40-25-141 shall be paid upon warrant of the commissioner of finance and administration, or county mayor, as the case may be, which warrant shall be issued upon properly authenticated and itemized bills of costs certified by the United States district attorney and judge holding the federal court, in the same manner as other similar costs are paid by the state or counties.