Usually it can- but subject to a few important restrictions for your protection. For starters, it must tell you that it is conducting a background check on a disclosure form that specifically lays out what information it will be looking at, which company will be conducting the check, and letting you know your right to have a free copy of whatever report it receives. This disclosure can’t have a release on it or any other extraneous information that might be confusing or misleading.
Further, before it can take any action against you (refusing to hire you, terminating your employment, etc) based on information it receives in such a report, it must tell you about the report, what it uncovered, and allow you to correct any false information that may have been reported.
Finally, your employer can’t use a background or credit check in any discriminatory manner. For example, if it’s going to run a background check on prospective employees, it’s not fair to only run them on, say, males or minorities.