It will depend on whether or not you have a conviction for immigration purposes, how your charges were dismissed (DEJ, Diversion, Drug Ct., etc.) and how long ago the case was. I would suggest that you contact an experienced immigration attorney for a face-to-face consultation and give him/her all of the facts surrounding your case. (S)he would then be in a better position to analyze your situation and advise you of your options.
The immigration consequences of criminal arrests can be among the most complex and important issues in immigration law. A marijuana-related charge or offense indeed may have very serious immigration-related ramifications, even if the criminal charge was dismissed. There are some circumstances in which the USCIS will treat a dismissal as a conviction (and even some circumstances in which it will treat a misdemeanor as a felony). There really is no substitution for obtaining court-certified copies of the all disposition documents and engaging an immigration attorney to review them in order to provide a legal analysis. Note also that a full set of court-certified disposition documents will be needed in the naturalization application process even if the dismissed offense will have no impact upon naturalization eligibility. Some immigration law firms, including mine, offer legal services on a "flat fee" basis so that a client will know the total expense from the very beginning, and a few immigration law firms, including mine, offer an initial consultation free of charge.
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