S.D. Codified Laws § 21-34-12

Nothing contained in this chapter shall affect or regulate the power of any court to punish contempts of such court for violation of any of its own rules, regulations, orders, judgments, decrees, commands, or judicial functions in cases where such jurisdiction inheres in the court as part of its judicial powers or jurisdiction, or is otherwise given to it as original contempt jurisdiction by statute, but the procedure in such cases shall be according to such inherent jurisdiction or statutory jurisdiction of such court as otherwise provided.