I would say that South Dakota does NOT have the castle doctrine in effect. Here are SD statutes:
22-16-34. Justifiable homicide--Resisting attempted murder--Resisting felony on person or in dwelling house. Homicide is justifiable if committed by any person while resisting any attempt to murder such person, or to commit any felony upon him or her, or upon or in any dwelling house in which such person is.
22-16-35. Justifiable homicide--Defense of person--Defense of other persons in household. Homicide is justifiable if committed by any person in the lawful defense of such person, or of his or her husband, wife, parent, child, master, mistress, or servant if there is reasonable ground to apprehend a design to commit a felony, or to do some great personal injury, and imminent danger of such design being accomplished.
Notice that the law does not define what reasonable grounds are to suspect that a felony, great personal injury or iminent danger is being committed.
A good example of Castle Doctrine is Oklahoma:
§21-1289.25. Physical or deadly force against intruder.
PHYSICAL OR DEADLY FORCE AGAINST INTRUDER
A. The Legislature hereby recognizes that the citizens of the State of Oklahoma have a right to expect absolute safety within their own homes.
B. A person is presumed to have held a reasonable fear of imminent peril of death or great bodily harm to himself or herself or another when using defensive force that is intended or likely to cause death or great bodily harm to another if:
1. The person against whom the defensive force was used was in the process of unlawfully and forcefully entering, or had unlawfully and forcibly entered, a dwelling, residence, or occupied vehicle, or if that person had removed or was attempting to remove another against the will of that person from the dwelling, residence, or occupied vehicle; and
2. The person who uses defensive force knew or had reason to believe that an unlawful and forcible entry or unlawful and forcible act was occurring or had occurred.
See the difference? In Oklahoma, someone breaking into your house is AUTOMATICALLY assumed to be doing so to cause death or great bodily harm and therefore it is AUTOMATIC that deadly force may be used lawfully to stop them.