The federal law governing employment background checks (Fair Credit Reporting Act) doesn’t prohibit employers from asking questions about criminal history on a job application. Ban the Box laws (check box on job applications about criminal history) are being enacted at the state, county and city level in response to this practice.
These questions can be very tricky to answer if you’re concerned about a mistake from the distant past or an arrest that didn’t result in a conviction. Also, there are many situations where a background screening company wouldn't be allowed to put this information in a background report even though an employer could ask on an application (i.e. arrests more than seven years old).
Ban the Box laws can be complex and vary depending on the state, county or city. The National Employment Law Project’s guide contains a comprehensive list of them.