S.D. Codified Laws § 23A-3-9
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 misdemeanor 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 misdemeanor in this state. The term "fresh pursuit" as used in this section shall include the pursuit of a person who has committed a misdemeanor in the presence of a law enforcement officer, and such officer is in instant pursuit.
SDCL 23A-3-9