Any conviction for an alien either in immigrant [green card] or nonimmigrant status such as L1 or H1b is always a potential problem for the alien. In this instance, you were convicted since you paid a fine. And contrary to what you may think. the case was not dismissed. Without knowing more about the facts of your case. If the New Jersey offense of conviction is deemed a deportable offense by ICE, you may be subject to deportation in future. If this case occurred recently, you may be able to return to the court to re plead hopefully to a safe harbor plea, but certainly under NJ law, there is a statute of limitations after which, you can no longer do so. I therefore suggest that you consult with a crimimmigration lawyer to help you properly analyze the immigration consequences of what you pled to. Do not file any paper work with CIS before you speak to a lawyer.
Answered on Mar 15th, 2013 at 11:48 AM