Married filing jointly, car that I use for work and business is on my wife name. For mileage deduction, Should I choose "I own the vehicle" or "This vehicle isn't mine"?

So we have 2 cars. One I drive is on my wife's name and one she drives is on my name. And as I looked back on my past year's return, I mentioned that very same car as not owning it.
So do i need to amend my last years tax return? Or I can say that from this year it has become my primary vehicle and I can go ahead with filing it as OWNING? Help will be appreciated. Thanks