Your employer can certainly ask. Without a court order, it is unlikely that your employer can force you to reveal it. On the other hand, in most states, including Arizona, your employer can fire you for "any reason" or no reason at all. "Any reason," however, is qualified by many factors -- you may not be fired for a reason that would violate your civil rights. If this issue becomes acute, you would be well advised to discuss it with an Arizona attorney who is experienced in the area of employment rights and wrongful termination. If you are a union member, you should also discuss this issue with your shop steward or other contact person, as may be appropriate.