Tennessee Code Title 6. Cities and Towns § 6-54-303

(a) In all municipal courts where the judge has entered a judgment for fines and costs, and same remain unpaid for thirty (30) days thereafter, the court is authorized by and through its clerk to issue execution thereon from the court in the same manner and methods as prescribed in title 26, chapters 1-3, and the clerks shall assess the same fees and costs as allowable to clerks of general sessions court.

(b) For purpose of service of a levy of execution or execution by garnishment, the police officers of the municipality are empowered to serve the same anywhere in the county.