I want to chime in to agree with the prior posts. I would suggest getting a protective order as well.
A little different approach
I have a bit of a different view than that have responded above. Having practiced family law for nearly 20 years (here is my site) I have come to realize that court orders are very effective at some things and not so good at others. One thing that they are not very good at is getting wacky people to stop acting wacky. While you may be entitled to a protective order based on her statement being interpreted as a threat to kill you (every state has a different law on exactly what must be proven), that may not be the most effective approach. Often times when it is simply annoying behavior self help is a better approach. For example, for someone who doesn't have children with their ex, simply change your phone number and don't let the ex know the new number. Just food for thought...
I think this is really necessary for you
Originally Posted by Wheelie
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The very next time it happens, call the police! Don't threaten her with calling - just call! That is the only way you will have the proof you need to file a restraining order.