Sorry, but maybe it's the L in me, but I disagree. I WOULD respond, but only to say (a) I did not threaten your life or threaten you in any way and have no idea what you are talking about and (b) I will be taking action to protect myself. Very business like and to the point. Nothing more.
My concern is that not responding might be argued to be an admission - You did not dispute it.
I stand corrected. Good advice. But after you tell her that, DO NOT CONTACT HER!