There isn’t a clear-cut answer to this question. State laws generally have some limits with how employers can use convictions in their hiring and promotion decisions. But there are also negligence issues to consider when bringing in an offender into the workplace.
The general rule is that there must be a clear connection between the offense and the job the offender would be performing for you to use their status as an offender as a reason to not hire them. For example, if an offender committed a sexual crime involving a child, then you are more than justified in not hiring them to be in a position where they’d be supervising or interacting with children.
It can be a good idea to consult with an employment attorney if you’re wondering what responsibilities you have when making hiring decisions taking criminal history into account.