In West Virginia back in the 1980's if you refused to sign the ticket, you were escorted straight to the closest courthouse and a magistrate either heard the case immediately or ordered you to appear on a certain date. I've heard the law has been changed so essentially it doesn't matter if you sign or not, the Officer just notes on the ticket that you refused to sign, but you are still legally bound to pay the ticket or dispute it in court.
Texas does give the officer the option of instander and taking you immediately to a judge. In my 14 years I only did that once. Just note they did not sign.