The defendant in a principal action by petition may bring in any person, including a codefendant, who is his warrantor, or who is or may be liable to him for all or part of the principal demand.

In such cases the plaintiff in the principal action may assert any demand against the third party defendant arising out of or connected with the principal demand. The third party defendant thereupon shall plead his objections and defenses in the manner prescribed in Articles 921 through 969, 1003 through 1006, and 1035. He may reconvene against the plaintiff in the principal action or the third party plaintiff, on any demand arising out of or connected with the principal demand, in the manner prescribed in Articles 1061 through 1066.