If the court was in error for not setting your matter to a contested hearing, the proper procedure would be to file a motion to set aside judgement.
I would advise you to consider retaining legal counsel to handle the matter as your initial attempt to resolve the matter without counsel was unsuccessful.
I agree with my colleague, if you never requested a hearing my mail, I would submit a "motion to set aside judgment," I would hire a traffic infractions attorney who can review your case.
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I have a feeling that the paper you sent in was a request for hearing by mail. Many courts will give you the option to write a letter to the court explaining why you think you did not commit the infraction, rather than taking the day off of work to appear in court before a judge. Generally, you cannot appeal the judge's ruling in your case if your hearing was conducted by mail.
It sounds like you were confused as to the purpose of the letter, and that may be a sufficient reason for the judge to grant a motion to vacate the committed finding and set your case for a contested hearing again.
I would certainly recommend speaking to an attorney about this situation if you are actually serious about getting the ticket off of your record. Part of the reason that you are in this situation is that you are not very familiar with the legal system, and you need more advice than someone can give in this type of forum.
WTF? What jurisdiction was this? The appropriate motion is CRLJ 60(b). Get a lawyer who knows how to handle this for you. I can be reached at 360-647-5251 or at firstname.lastname@example.org.