If you are looking for an Oklahoma background check resource that can be used to look into someone's past family life, you can contact the Vital Records office of the Department of Health and make a request for marriage, divorce or other similar records. They are open to the public though it can take up to a month to get a response and it will cost you $15 for each request.
Oklahoma Criminal History
The open records policy extends to the state justice system, and you can make similar requests to see someone's criminal record. You can make a $15 search using the forms from the Oklahoma State Bureau of Investigation website, sent in by mail or fax. You can't do searches right online. For other related records, you can use the Oklahoma State Courts Network for a wide variety of court case files. These are free to search for anyone.