As a North Dakota background check resource, the Vital Records office can be bit of assistance but not all records are open to the public. Birth and death records will only be given out if you are a direct relative. But if you want to know if someone has been married, you'll want to find a marriage or divorce record and they are kept by the county's Clerk of Court or County Recorders offices. You have to contact them for access requirements.
Interested in someone's potential criminal past? The best North Dakota background check resource for that is the Criminal Justice Information Sharing System for the state, but it does not allow you to make enquiries about other people unless you are on authorized employer doing hiring screening. If that applies to you, then you have to submit a complete fingerprint card to the Criminal Justice office in Bismarck.