Tex. R. Civ. P. 38

As amended through February 20, 2024
Rule 38 - Third-party Practice
(a)When Defendant May Bring in Third Party. At any time after commencement of the action a defending party, as a third-party plaintiff, may cause a citation and petition to be served upon a person not a party to the action who is or may be liable to him or to the plaintiff for all or part of the plaintiff's claim against him. The third-party plaintiff need not obtain leave to make the service if he files the third-party petition not later than thirty (30) days after he serves his original answer. Otherwise, he must obtain leave on motion upon notice to all parties to the action. The person served, hereinafter called the third-party defendant, shall make his defenses to the third-party plaintiff's claim under the rules applicable to the defendant, and his counterclaims against the third-party plaintiff and cross-claims against other third-party defendants as provided in Rule 97. The third-party defendant may assert against the plaintiff any defenses which the third-party plaintiff has to the plaintiff's claim. The third-party defendant may also assert any claim against the plaintiff arising out of the transaction or occurrence that is the subject matter of the plaintiff's claim against the third-party plaintiff. The plaintiff may assert any claim against the third-party defendant arising out of the transaction or occurrence that is the subject matter of the plaintiff's claim against the third-party plaintiff, and the third-party defendant thereupon shall assert his defenses and his counterclaims and cross-claims. Any party may move to strike the third-party claim, or for its severance or separate trial. A third-party defendant may proceed under this rule against any person not a party to the action who is or who may be liable to him or to the third-party plaintiff for all or part of the claim made in the action against the third-party defendant.
(b)When Plaintiff May Bring in Third Party. When a counterclaim is asserted against a plaintiff, he may cause a third party to be brought in under circumstances which under this rule would entitle a defendant to do so.
(c) This rule shall not be applied, in tort cases, so as to permit the joinder of a liability or indemnity insurance company, unless such company is by statute or contract liable to the person injured or damaged.
(d) This rule shall not be applied so as to violate any venue statute, as venue would exist absent this rule.

Tex. R. Civ. P. 38