Texas Health and Safety Code - HEALTH & SAFETY § 822.013. Dogs or Coyotes That Attack Animals

(a) A dog or coyote that is attacking, is about to attack, or has recently attacked livestock, domestic animals, or fowls may be killed by:

(b) A person who kills a dog or coyote as provided by this section is not liable for damages to the owner, keeper, or person in control of the dog or coyote.

(c) A person who discovers on the person's property a dog or coyote known or suspected of having killed livestock, domestic animals, or fowls may detain or impound the dog or coyote and return it to its owner or deliver the dog or coyote to the local animal control authority.  The owner of the dog or coyote is liable for all costs incurred in the capture and care of the dog or coyote and all damage done by the dog or coyote.

(d) The owner, keeper, or person in control of a dog or coyote that is known to have attacked livestock, domestic animals, or fowls shall control the dog or coyote in a manner approved by the local animal control authority.

(e) A person is not required to acquire a hunting license under Section 42.002, Parks and Wildlife Code, to kill a dog or coyote under this section.