Articles of Partnership generally cover most aspects of a business co-ownership between two people. The only thing not covered by the partnership articles is the buyout price of the company.
The Uniform Partnership Act, recognized by more than forty states, states that "a partnership is an association of two or more persons to carry on as coowners a business for profit" (UPA 6[11]).
If the car is paid off. You and the co-owner can go to DMV and register the car in one name.