It does vary by state and in the US the company usually has the upper hand BUT..

I MOST cases, they must receive a signed release from the employee. Asking in an interview is just not acceptable, if the employee refuses to answer he/she is automatically deemed guilty by default for refusing to answer.

If the new employer contacts the old employer, it is illegal for the old employer to give out detailed information as to why you were fired. If he does give out this information, he can be sued by the employee

Therefore, in order to obtain ANY criminal background information, the employer must have a signed release.

They CAN refuse to hire anyone who refuses to sign a release for a criminal background check though.

Been to court on it, got the t-shirt, it's old and faded now though.