That's legally actionable for her to drive the police straight to your door.
This is factually incorrect.
One of my friends had a rather persistent suitor (i.e. stalker). She went to the police, in liberal Massachusetts where violence against women is a popular political cause. The police were unable to do anything until there was a threat of violence, or a restraining order. They did provide free legal resources for her to get a restraining order, but until the restraining order was in place (which was made to happen pretty quickly), there was no way to prevent the creep from communicating with her.
Or course, a restraining order is a civil matter. Breaking a restraining order is a police matter.
But the claim that that sending communication is "legally actionable" is simply incorrect.
I agree with the sentiment that you should stop communicating with this woman who clearly doesn't want to interact with you. But I disagree with the fact that they feel like lying to you is warranted.
The fact is that you have no reason to worry legally... and that you could likely be a much bigger jerk (if you chose) without any real fear of legal consequences.
You can back away because you are a decent person, not because you are afraid of the police.