There is nothing in being a cosigner that makes you a co-owner. If your state allows a notation on the title that so-and-so cosigned for a loan, that would not make the cosigner into a co-owner.
If the state allows a cosigner to be named on the title along with the lender, then the cosigner would likely gain repossession rights in the event of default; if only the lender is named, then only the lender can repossess.

