Under the Federal Fair Credit Reporting Act (FCRA), you must be told if information in your credit report or other type of consumer report has been used against you.
Anyone who uses such a report to deny you employment must tell you, and must give you the name, address and phone number of the agency that provided the information. You have a right to know what is in your file. You should be given the report by the offending agency free of charge.
States may enforce the FCRA and many states have their own consumer reporting laws. In some cases, you may have more rights under state law. For more information, contact your state or local Consumer Protection Agency or your state's attorney general.
Remember, however, that much of the information gathered by background checking companies is contained in public records (e.g., criminal convictions). If what was uncovered during the background check was something of this nature, you still need to know about it and make sure that there is no case of mistaken identity involved.
Next step? Politely ask the employer why you have not received the formal offer of employment. If you have any reason to believe from the answer provided that the background check is the reason, ask for a copy of it. If they resist, tell them that you really have no choice but to contact the office of the state attorney general, as you need to find out what could possibly be in a report of any kind that would preclude you from being offered a job. Otherwise, how can you get the record corrected?