Texas Local Government Code - LOC GOV'T § 86.024. Failure to Execute Process

(a) If a constable fails or refuses to execute and return according to law a process, warrant, or precept that is lawfully directed and delivered to the constable, the constable shall be fined for contempt before the court that issued the process, warrant, or precept on the motion of the person injured by the failure or refusal. This section does not apply to actions brought under or that could have been brought under Chapter 34,  1 Civil Practice and Remedies Code.

(b) The fine shall be set at not less than $10 or more than $100, with costs. The fine shall be for the benefit of the injured person. The constable must be given 10 days' notice of the motion.