Am I liable if I co-sign for a car loan for my 25 yr old daughter who has a separate insurance policy in her name only?

you are of course liable for the note/loan should she stop paying.......if you are a co-signer to the note only and not a co-owner, then your liablity stops at the note.....if you are however a co-owner, of the vehicle as well, then you also have equal liablity(with your daughter) regarding the operation of the vehicle..........