Tenn. Code Ann. § 67-1-1203

Garnishments may be issued and executed by the sheriff, any deputy sheriff or constable in the same manner as garnishments are issued and executed on executions at law. Before issuing a garnishment, the sheriff, any deputy sheriff or constable shall cause such distress warrant to be entered on the docket of any court of general sessions or circuit court of the county, and the procedure in the execution of such garnishment shall be the same as now provided by the statute for the execution of garnishments in civil cases.