An employer can request a copy of your credit history to determine whether to hire or terminate you as part of a background check. They absolutely must get your permission first to run your credit report.
If your employer sees that the report is used negatively against you, he or she should give you a copy of the report and let you know your right to dispute it and share the contact information of the company that made the report. It is very important that you know that your employer cannot use your credit report to discriminate against you, nor to deny employment based on your race, sex, religion, and ethnicity.