An employer that rejects everyone with a conviction from all employment opportunities is likely engaging in discrimination. If an employer only drug tests the job applicants who have criminal records, then the employer may expose themselves to discrimination claims and.Felony Background Checks. Criminal Operations conducts felony background checks for Bexar County. While in the process of filling a vacant position, you discover that an applicant has a criminal record. Background Checks: Criminal History and Discrimination in Employment. Employment Discrimination Based on Criminal Records. What is illegal discrimination? Operations in order to maintain their TCFP certification. Still, businesses must wield them with care to avoid potentially discriminatory hiring practices.