This is a very common question. We aren’t employment lawyers, but I think we can help.
Unfortunately there isn’t a one-sized fit-all answer because every job is different.
What I can say is Texas is an “at-will” state meaning in most cases an employer can terminate you for a good reason, for a bad reason, or for no reason at all. I point this out to underscore how powerless most people are to begin with when it comes to their jobs in the first place. So it’s possible that you can do everything right and still be shown the door. But experience tells me that most employers aren’t in a big hurry to get rid of good help.
Some jobs may require disclosure and some jobs may not. A good place to start is always your employee handbook or employee manual if you have one. Be sure you understand your company’s policy.
So What Do I Tell Them?
I can’t think of any rule, law or regulation — even if you work for the government — which requires you to disclose anything other than the arrest itself. Even if you work for law enforcement they have internal-affairs mechanisms to deal with getting information from an accused (but that’s pretty well outside the scope of today’s discussion.)
Anytime you tell others about the facts of the case you are creating another witness who could come to court and testify against you. My guess is disclosure of the arrest in and of itself would normally be sufficient to put your employer on notice of your situation.
Professional Licensing Bodies
Also if you have a license such as a medical license, nursing license, or commercial driver’s license (as examples), you may also want to make sure you know the rules for reporting arrests that the state may require. Even though your employer may not care, a professional licensing agency certainly may!
Familiarize Yourself with the Proper Terminology
You should understand the precise terminology that your company may be asking for as well as understand the precise status of your situation — whether it be arrest, indictment, pre-trial, or whatever the case may be.
It is my experience that most employers are fairly respectful of the judicial process and don’t require you to confess to keep your job. Usually they just want to keep their finger on the pulse of your case and aren’t interested in the details until your case is over, and sometimes they may not have much of an interest at all.
Obviously if your arrest is related to your workplace then it’s a completely different ballgame. In any event, if you have any questions about these issues you should consult an attorney that can help you in complying with your workplace policies.