What can a cosigner do after a car is repossessed Can they sue the primary signer?

Seems pointless to even consider. If the primary signer didn't have enough funds to make the car payments, they probably will not have enough funds to pay any lawsuit you charge them with. Fact is, if the primary signer defaulted on payments, then the cosigner would be responsible for making them - If repossession occured, then it was due to the fault of the cosigner .. can't sue yourself.