According to the Texas C-BAR's Nonprofit Guide to Employment Law Issues in Texas (see link below), there is no law requiring employers in Texas to provide bereavement leave. This does not surprise me: Sick leave and bereavement leave policies are usually left up to individual employers in most states.
But I don't practice law in Texas, so don't take what I say here as legal advice. It's just my two cents on your question in light of general principles of law. If you need legal advice, please consult a lawyer who holds Texas licensure. That's not me.