Whenever any acts in violation of the penal laws of the United States committed by any person upon any Indian reservation within this state shall constitute a crime under any law of the State of South Dakota, concurrent jurisdiction is hereby expressly reserved to the State of South Dakota to arrest, prosecute, convict, and punish any person committing any offense under the laws of the State of South Dakota, even though the acts constituting such offense may also constitute an offense under the laws of the United States of America.
SDCL 23A-16-1