Thank you. The reason that I asked is that Texas is an "at will" employment state. At-will employment means that without a contract, you have no contractual or other right to employment with the company. The company is entitled to fire you for any reason: a good reason, a poor reason, or no reason at all--as long as the company does not fire you for an illegal reason (race, gender, age, religion, etc...). But it extends beyond firing, to hiring, promotions, demotions, wage cuts and raises, disciplinary actions, and even scheduling. Unless you can show that this was done in violation of a contract, union agreement, or a clear violation of an unambiguous and binding clause against the employer, or that it was done because of some minority status (age, race, gender, religion, disability) that you have, then they do have this discretion.
Now as a governmental employee, you have a bit more rights, in that you have the right to "due process" prior to being terminated. That essentially means that you're given a hearing and explanation of why you'd be terminated, and an opportunity to object. But you can still be terminated. And there's no law that says that your employer can't ask for your tax return. I agree that it's irrelevant and frankly strange that they're doing so, and I would complain higher up the ladder if you can, but if no one overturns this matter, the employer can still require that you do so.
I know this is probably not what you wanted to hear, but it is the law. I hope that clears things up anyway. If you have any other questions, please let me know. If not, and you have not yet, please rate my answer AND press the "submit" button, if applicable. Please note that I don't get any credit for the time and effort that I spent on this answer unless and until you rate it positively (good or better). Thank you, ***** ***** luck to you!