Employment discrimination generally exists where an employer treats an applicant or employee less favorably merely because of a person's protected class. If an employer only drug tests the job applicants who have criminal records, then the employer may expose themselves to discrimination claims and.A Houston employment background check involves researching an applicant's qualifications, educational attainment, employment history, and criminal record. You can submit your complaint online with the Employment Discrimination Complaint Form. You probably need to get ahead of it and inform your potential employer before the background check. The time it takes for an employer to run a criminal background check in Texas can vary. BY TX LAW, if an arrest is expunged, and a job app asks me to disclose any arrests, even those expunged, do I have to or not? Regarding criminal record discrimination, employers may not discriminate against job applicants with similar criminal records based on protected classes. May not be discriminated against in hiring or continued employment on the basis of an erased criminal record. In the labor market, people with criminal records struggle to find work.