Legal Question in Immigration Law in New York

Yes, it can. You shall consult a good immigration lawyer before applying for naturalization.

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The fact that your conviction is a misdemeanor is not the key. What you need to look at is the specific law under which you were convicted. Generally, if your conviction is for a crime that involves "moral turpitude," then regardless of whether it is a misdemeanor or a felony, you will likely have issues. Before applying for naturalization, you should consult an immigration lawyer.