Texas Local Government Code - LOC GOV'T § 89.004. Presentation of Claim

(a) Except as provided by Subsection (c), a person may not file suit on a claim against a county or an elected or appointed county official in the official's capacity as an appointed or elected official unless the person has presented the claim to the commissioners court and the commissioners court neglects or refuses to pay all or part of the claim before the 60th day after the date of the presentation of the claim.

(b) If the plaintiff in a suit against a county does not recover more than the commissioners court offered to pay on presentation of the claim, the plaintiff shall pay the costs of the suit.

(c) A person may file a suit for injunctive relief against a county. After the court's ruling on the application for temporary injunctive relief, any portion of the suit that seeks monetary damages shall be abated until the claim is presented to the commissioners court and the commissioners court neglects or refuses to pay all or part of the claim by the 60th day after the date of the presentation of the claim.