under CT law, is a parent liable for property damage caused by minor child

Offering half of the deductible was probably a fair offer. In CT, parents are not automatically responsible for the negligence of their children by common law. There are circumstances where parents can be responsible. An example might be if you knew that your daughter had a habit of kicking in car sunroofs, etc and you knew she was going out to do just that on the day in question, and you did nothing to stop it. Another example, might be if your daughter intentionally or maliciously destroyed personal property. There is a statute you can look at that makes parents jointly responsible with their kids. (Connecticut General Statute 52-572). In this circumstance, it looks like an innocent mistake so these examples would not apply. The parents could bring a claim against your daughter for negligence, but she will be held to the standard of an average 12 year old. 12 year olds do stuff like that. At least, I did anyway. Also,it looks like the parents might be negligent themselves and/or their own daughter probably equally at fault.