Criminal histories are the most important information from a Texas background check resource, and there are a few different options you can use for this.
The Texas Department of Public Safety offers a criminal search database that is open to the public that contains arrests, prosecutions and case dispositions for anything over a Class B misdemeanour in Texas. There are fees for each search and you will have to register with your own information before you can use the system. They also have a separate database for sex offenders that can be used by anyone.
Other Record Sources
Vital records are not a practical Texas background check resource because they are confidential for at least 25 (or 75 for birth records). Family members will have access though. Marriage or divorce verifications (not actual records) are open to the public for a $20 fee from the Vital Statistics office.