A Houston employment background check involves researching an applicant's qualifications, educational attainment, employment history, and criminal record. HireRight is a leading global provider of on-demand employment background checks, drug testing, Form I-9 and employment and education verifications.Apply to Housekeeper, Warehouse Associate, Driver and more! This policy sets forth requirements for background checks for employment and to provide guidelines for the hiring of employees. Candidates sign a Certify and Submit form authorizing the City of Houston to check background information for employment purposes. Background checks are an essential part of the hiring process. Here's what to know about how to run background checks in Texas. References and Background Checks. Note: under Texas law, it is legal for a person to record a conversation without the knowledge or consent of others. A background check helps you make informed hiring decisions and build a team you can trust.