Can Fake FB Profile Be Investigated By The Police?

[Shanna]

I made a fake fb fake name no picture, no friends, said I lived in a different country... I saw a girl I went to high schools profile and she was bragging about being on welfare so I messaged her saying that she was going to be a whore just like her mother and that she didn't know who fathered her children and she'll be working at mcdonalds the rest of her life. Her mother gets on her fb and emails me back saying when she finds out who I am she's going to kill me and that I better start making funeral arrangements so that they can bury me if they find the body... Could what I did be called Harrassment and would the police look into it because that's the only way she would be able to find me and I know she's been to jail before or will she not report it since she threatened to kill me and nothing I said was threatening plus I deleted the account completely