Tex. R. Civ. P. 622
As amended through August 27, 2024
An execution is a process of the court from which it is issued. The clerk of the district or county court or the justice of the peace, as the case may be, shall tax the costs in every case in which a final judgment has been rendered and shall issue execution to enforce such judgment and collect such costs. The execution and subsequent executions shall not be addressed to a particular county, but shall be addressed to any sheriff or any constable within the State of Texas.
Tex. R. Civ. P. 622