No, it is NOT a crime to tell someone to go kill themself--it's simply not anything prohibited by law. Anyone can say any cruel or immature thing they like to anyone else. She can't threaten that *she* will kill you, but that is a very different statement and situation.It's also not anything you can sue over, both because the other person has a right to do this and because you are not injured by it other than hurt feelings or being upset--but there is no compensation for hurt feelings or being upset.