I represent a lot of clients who have warrants here in Massachusetts who are involved in family Court. I was waiting for someone from Texas to step in and answer this, but i think it is safe for me to say that as a general rule it is better to take care of the warrant before you go into family Court. It is very hard to assert your rights in family court while you are being escorted out in shackles. I would also advise you to consult an attorney as you will be able to share a lot of details that you have not given us here. Good Luck.
What kind of warrant--traffic ticket or something more serious? If it's a traffic ticket warrant, unless somebody alerts the bailiffs, I doubt it's going to cause you a problem. But if your opponent in the suit knows about the warrant, then you might run into a little trouble.
It's not like the Harris County Jail, where if you go to visit an inmate, they take your ID and check you for a warrant. At the same time, I've seen people get taken into custody in the Family Law Building, and usually that's because somebody let the bailiffs know the person had a warrant. Traffic ticket from Brownsville or other city far away?--you probably don't need to worry about the Harris County Sheriff's Office taking you into custody while they wait for that city to send somebody to drag you back there to face your ticket charge.
Better take care of that warrant. If it's a Class B or higher warrant, start talking to bonding agents in the city where the warrant was issued. If it's a traffic ticket warrant, find traffic ticket lawyers in that city--many cities allow the lawyers to lift the warrant on an attorney bond.
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Unfortunately the answer is, it depends.
It mostly depends on whether anyone in authority finds out about the warrant and cares to do anything about it. They are not checking IDs at the door and aren't looking for it, but if you cause a problem or someone alerts the judge or bailiff to the warrant they could arrest you.
I have had clients appear for family court with multiple warrants for fairly rough charges and walk back out at the end of the hearing. I have also seen people arrested on a warrant before the hearing even started, but that is rare.
Either way having a lawyer will help as they can run interference for you and will know whether the judge is the kind of judge that likes to arrest people or not.
I had the misfortune of representing a client who was in court in Harris County, Texas, on a contested custody matter. There was a warrant issued against him that he was not aware existed. Opposing counsel alerted the bailiff of the warrant, as she was informed of it by her client, who lived in the house and apparently received notice of the warrant by mail and did not tell her soon-to-be ex-husband. My client was immediately handcuffed and removed from the courtroom before the proceedings began. Absolutely no testimony or explanation was allowed. He did not even know why he was being arrested. The judge informed all counsel in the case that if he is aware of an existing warrant, the proceedings will end and the person removed and taken to jail. Period. He maintained that this is absolute and he had no discretion.
I would work diligently to remove the warrant before appearing in court, or alternatively, appear knowing that if anyone tells the bailiff, judge or court personnel about the warrant, you are likely to be escorted directly to jail.