Does a cosigner have any liability if the owner of vehicle has an accident?

You are certainly responsible for the actions of primary to the extent of the loan.

No.

In no way could a person be held legally responsible for an accident on grounds that they were the cosigner of the loan that procured the vehicle.

You are neither responsible, and the other side of the issue, nor at any particular risk of loss. Even if the owner is entirely liable, and unresponsible to the degree of not having insurance or other assets to pay for damages they caused, any judgment against them would probably try to get other $ first, and could only try and get to the equity, that is the amount of value above the amount of the secured loan on the car, if any, AFTER paying off the secured creditor - which is the loan you co-signed, releaving you of any responsibility. But, it would make just as much sense, and maybe more, for someone to sue the bank that made the loan as to try and get you, a co-signer of the loan, involved.