Unless otherwise precluded by law - for example, employers who are involved in the care of children, the elderly or disabled, are precluded from hiring persons with certain criminal backgrounds - you can hire whomever you want. There are employer- and employee-specific issues - for example, you wouldn't necessarily want to hire somebody with a felony drunk driving conviction as a delivery driver, or with an embezzlement conviction as a bank teller.
So you can check any restrictions that apply to your business enterprises, craft a policy that observes any legal restictions and serves your needs, and follow that policy. It may help to have an employment lawyer draft the policy for you such that you can be reasonably sure that it is complete, understandable, and enforceable.

