Tex. Civ. Prac. & Rem. Code § 34.070

An officer against whom a judgment has been taken under Section 7.001, 7.002, 34.061, 34.063, 34.064, 34.065, 34.066, or 34.067 or under Section 86.023, Local Government Code, or a county that has paid the judgment on behalf of the officer under Section 34.069, has a right of subrogation against the debtor or person against whom the writ was issued.