Tex. Agriculture Code § 142.009

(a) The sheriff or the sheriff's designee shall impound an estray and hold it for disposition as provided by this chapter if:

(1) the owner of the estray is unknown;

(2) the sheriff or the sheriff's designee is unable to notify the owner;

(3) the estray is dangerous to the public;

(4) the estray is located on public property and after notification is not immediately removed by the owner; or

(5) the estray is located on public or private property and is not redeemed not later than the fifth day after the date of notification, unless the sheriff or the sheriff's designee determines that the owner of the estray is making a good faith effort to comply with Section 142.004(a).

(b) After impounding an estray, the sheriff or sheriff's designee shall prepare a notice of estray stating at least:

(1) the name and address of the person who reported the estray to the sheriff;

(2) the location of the estray when found;

(3) the location of the estray until disposition; and

(4) a description of the animal, including its breed, if known, color, sex, age, size, markings of any kind, including ear markings and brands, and other identifying characteristics.

(c) The sheriff or sheriff's designee shall file each notice of estray in the estray records in the office of the county clerk.

(d) If the owner of the estray is unknown, the sheriff or the sheriff's designee shall make a diligent search for the identity of the owner of the estray, including a search in the county register of recorded brands, if the animal has an identifiable brand. If the search does not reveal the owner, the sheriff shall post a notice of the impoundment of the estray on the public notice board of the courthouse and advertise the impoundment of the estray:

(1) in a newspaper of general circulation in the county at least twice during the 15 days after the date of impoundment; or

(2) on the county's Internet website for at least 15 days after the date of impoundment.