Something to consider...If you file a claim through your insurance company, a deductible may apply even though you were not at fault. Check with your insurance company on that. They may be willing to subrogate and recover your deductible. If you file a claim with the driver-at-fault insurance company, there will be no deductible.
Firetrux makes a real good point about diminished value, especially since your state (CT) is a diminished value state. You're entitled to it by law but may have to fight for it. Read up on it here: