The main South Dakota background check resource for family-oriented documents is the Vital Records office in Pierre. You can also get vital records at the Register of Deeds office in your county. Plain-paper copies (non-certified) are issued to the general public so you can ask for anyone's marriage, divorce, birth or death records providing you fill out the application and pay the search fee.
You have two South Dakota background check resources for criminal histories, though one is not really open to everyone. The Division of Criminal Investigation has a fingerprint-based system for record checks, so you cannot get someone's record without their knowledge though it is open to anyone who can get a fingerprint card completed. Additionally, you can get access to civil court records through the Clerk of Court office in your county. There are fees for these searches as well.