Last month I was teaching my friend how to drive.  while she was
learning, she hit a tree and totalled my car.  she's over 18, so a
learners permit was not required for her to drive as long as i (who
have been driving for over three years) was in the passenger seat. 
Now she is giving me flak and telling me that it's my fault for
letting her drive in the first place and refuses to pay the entire
amount of the damage (only approximately half).  Who is legally
required in the state of CT to take responsibility for the accident? 
If it makes a difference, the car is registered in the state of MA,
and my drivers license is also from MA.  The accident took place on my
property in CT (she backed into a tree on the way out of my driveway
by flooring the accellerator instead of the brake when i told her to
stop).

This is not the place for legal advice.  You only get opinions here.
When you let her drive you assumed the risk that something might
happen, and it did.  If you have insurance on your car you can make a
claim.  It would seem fair for her to cover the deductible, if any.