Q: Shoplifting in New York City 6 years ago, affect her US citizenship application?

A: This will have a negative impact on her chance to stay in the U.S. Marriage to a U.S. Citizen is insufficient to protect her. She might be subject to removal proceedings. You need to have an in person consultation with an experienced immigration attorney immediately!

A: Under immigration law, an applicant for naturalization must prove good moral character for a five year period prior to filing the N-400. (While USCIS can go back more than five years in the exercise of discretion, they usually do so only in cases of more serious offenses or multiple convictions.) Any time that a person was in probation or some form of court supervision counts as part of the prior five years. Here, according to what you say, your cousin's court supervision ended in September of 2013; her N-400 will be filed well after the five years period. I sincerely doubt that she will be denied naturalization based on what sounds like an ACD, which does not even count as a conviction, since in an ACD, one need not plead guilty or admit the crime. In other words, with an ACD, there was never a conviction. Even if there was a conviction, as I said, she would not likely be denied naturalization. However, it is very important that she state the fact of the arrest and the disposition. I would immediately obtain certified copies of the court documents, especially the judgment, as this will let you and your lawyer know exactly what happened, and provide all the correct information. Good luck!