No. Class C traffic citations should not effect your probation. Make sure to handle the citations promptly and do not let them hit warrant status.
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Technically it is a violation because it is a violation of law. However, if you are on probation for an offense that is a class B or above, they will not use a traffic violation such as this to affect the probation.
While most traffic violations are Class C misdemeanors in Texas, minor traffic violations will generally not result in a revocation of probation for Class B misdemeanor charges and higher.
Generally minor traffic violations do not cause your probation to be violated; however, it depends on how tightly the probation agreement is drawn. Some probation agreements require that you "obey all laws" regardless of how minor, and you could theoretically violate even with a small traffic offense. The reality of the matter is that most traffic matters would never appear on a probation officer's radar screen and therefore not likely cause a problem, although most probations require that a probationer self-report.