There is, however, a "ban the box" movement in a plurality of states, banning employers from asking potential employees about a criminal record.
With the internet documenting all public information, however, it's normally trivial for an employer to do a little research and find the employee's record.
Typically, an employer can run a criminal background check in a "ban the box" jurisdiction, but only later in the process (for example: after completing interviews and provisionally deciding this is someone you'd like to hire). There may also be other rules in place about how you can use information from the background check, and what you have to do if you decide to revoke the offer of employment based on the result of the check.
You just can't ask on the application form. You can ask later on in the process though. The idea is to give people with criminal records at least a fighting chance of getting interviews.