S.D. Codified Laws § 23A-3-10
Current with legislation signed by the governor on or before 3/6/2024
Any member of a duly organized state, county, or municipal law enforcing unit of another state of the United States who enters this state in fresh pursuit, and continues within this state in such fresh pursuit, of a person in order to arrest the person on the ground that the person is believed to have committed a felony in such other state, shall have the same authority to arrest and hold such person in custody, as has any member of any duly organized state, county, or municipal law enforcing unit of this state, to arrest and hold in custody a person on the ground that the person is believed to have committed a felony in this state.
SDCL 23A-3-10