What are a cosigner's rights when a car is repossessed?

Rights? they have the obligation to pay if the primary signator defaults (which is what caused the repo). they may or may not be on title, which determines some of their property rights. You would need to check local (state) laws regarding this. You really take on a serious risk when co-signing and should do so carefully. If the person who bought the car defaults, then you have to pay for it or have it go on your credit report as a bad debt. If you credit history was good, this can really mess you up as most credit issuers are using other companies records to base their own interest rates. You can get royally done in from higher interest rates. So, if you can afford to, get that car redeemed (pay it current and get it back) and make sure that the payments are on time from here on out.