S.D. Codified Laws § 15-6-14(a)
At any time after commencement of the action a defending party, as a third-party plaintiff, may cause a summons and complaint to be served upon a person not a party to the action who is or may be liable to him 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 serves the third-party complaint not later than ten 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 with the summons and third-party complaint, hereinafter called the third-party defendant, shall make his defenses to the third-party plaintiff's claim as provided in § 15-6-12 and his counterclaims against the third-party plaintiff and cross-claims against other third-party defendants as provided in § 15-6-13. 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 as provided in § 15-6-12 and his counterclaims and cross-claims as provided in § 15-6-13. Any party may move to strike the third-party claim, or for its severance or separate trial. A third-party defendant may proceed under § 15-6-14 against any person not a party to the action who is or may be liable to him for all or part of the claim made in the action against the third-party defendant. The court may render such judgments, one or more in number, as may be suitable. As among joint tort-feasors against whom a judgment has been entered in a single action, the provisions of § 15-8-15 apply only if the issue of proportionate fault is litigated between them by cross-claim, counterclaim, or third-party claim in that action.
SDCL 15-6-14(a)