Legal Question in Immigration Law in New York

Assuming that your criminal record consists of only the one arrest you mention, in order to be deported for petit larceny or disorderly conduct the crime would have to be classified as a crime of moral turpitude, and the commission of the crime must have occurred within five years after your date of admission to the United States. Furthermore, the crime for which you were convicted must provide by statute that a sentence of one year or longer may be imposed. A close review of the full criminal record and the exact wording of the state statute would be required in order to determine whether your criminal history would meet these requirements.

A noncitizen's criminal record is relevant to an application for naturalization because one of the requirements for naturalization is good moral character within the statutory period, which is usually the preceding 5 years. If the crime occurred outside of that statutory period it is less important, but can still be considered.

I suggest you consult with an attorney so that the specifics of your situation can be analyzed.