S.D. Codified Laws § 1-1-2
Jurisdiction of the lands and their appurtenances which have been or may be acquired by the United States through donations from this state or other states or private persons or which may have been acquired by exchange, purchase, or condemnation by the United States for use of the Battle Mountain Sanitarium reserve in Fall River County; Fish Lake in Aurora County; Wind Cave National Park; the Badlands National Monument or park, and for other public purposes of the United States is hereby ceded to the United States and all such prior grants or donations of this state are hereby confirmed; provided however, that all civil or criminal process, issued under the authority of this state or any officer thereof, may be executed on such lands and in the buildings which may be located thereon in the same manner as if jurisdiction had not been ceded.
SDCL 1-1-2