What happens if you admit to a murder and then get arrested for it? please read my description?

I am doing a project for my english final and we have to do a court scene based on edgar allan poes "the tell tale heart" so I am asking a few questions. What happens if you admit to a murder and then get arrested for it? Do you still go to court. In the story he admitted to the police that he did commit murder at the old mans house. But what happens after that. Do they still go to court? I kind of want to make it so someone states he admitted to the police at his home. But then he pleas not guilty to the crime at the court and then he tells where he was ect. Then he gets so nervous he confesses again. But could this even happen. It has to be CONSISTENT with the legal system. Thanks!