The fact is that unless not running background checks on exisiting workers constitutes some form of legally actionable discrimination, it is legal. In other words, if running such checks on new employees only is due solely to their race, religion, disabiltiy, age (over 40), gender, or nationality, then that would create problem. Otherwise, absent an employment contract or union agreement to the contrary, most work relationships are "at will" which means that an employer can set the conditions of the workplace much as as it sees fit.