Yes, they would need to initiate a court proceeding. Not sure how they find out in general. But in some cases in the news, this happened to ex-Nazis who hid their full activities during the Holocaust and War, and were later found out by anti-Nazi activists. This is a naturalization lying issue because there are questions on immigration and naturalization forms that ask about participation in the Nazi party. (Of course, if they had told the truth, they would also not have been naturalized, and probably prosecuted; but that's another issue.) I have the feeling that this kind of thing mostly happens when someone is already being investigated for wrongdoing.