If you cosigned a leased car for your daughter and the car and insurance are in her name are you responsible as cosigner for any liability over the covered insurance amount in the event of an accident?

No. Y-THINK-Y * Ordinarily a cosigner would not be liable for anything other than the lending agreement. However, responsibilities incurred by all parties when a vehicle is under lease can be quite different than the purchasing a vehicle. It would be prudent for the cosigner to read the leasing contract very carefully and perhaps seek legal advice if they are unsure of the terms of the contract.