S.D. Codified Laws § 1-1-6
The consent of the State of South Dakota is hereby given to the acquisition by the United States by purchase, gift, or condemnation with adequate compensation, of such lands in South Dakota as in the opinion of the federal government may be needed for the establishment of national forests, the production of timber, the preserving of the navigability of navigable streams, or to prevent soil erosion, provided that the jurisdiction of South Dakota, both civil and criminal, over persons upon such lands shall not be affected or changed by their permanent reservation and administration for the purposes herein referred to, except so far as the punishment of offenses against the United States is concerned, the intent and meaning of this section being that the State of South Dakota shall not by reason of such reservation and administration lose its jurisdiction nor the inhabitants thereof their rights and privileges as citizens, or be absolved for their duties as citizens of the state; and provided, that the State of South Dakota shall retain a concurrent jurisdiction with the United States in and over such lands so far that civil process in all cases and such criminal process as may issue under the authority of the State of South Dakota against any person charged with the commission of any crime within or without said jurisdiction may be executed thereon in like manner as if this statute did not exist.
SDCL 1-1-6