Something that doesn't appear to have occurred to you; the schools OWN RECORDS will tell them immediately that you had been registered there before.
Is it a crime for which you will go to jail? Maybe, maybe not. Hard to say since you refuse to answer the questions posed to you, which were asked for a reason.
But even if not a crime and not illegal, that doesn't mean that there can be no possible repercussions. As indicated, lying even by omission on an application can result in your being thrown out of school and possibly your degree yanked. Which will follow you to every other school you apply to.
Given that you cannot possibly hope to avoid discovery, is it really worth it to try to hide whatever you're trying to hide?