You financed a car but are moving to a different state?

You let the finance company know your new address, and be sure to transfer your auto insurance coverage to the new state so there are no gaps.

Also, if you are moving from a title-holding state (Such as Ohio) you need to tell the clerk at the DMV/BMV. They will put a request back to your original state for the real title, and the states vary on how they handle your registration at that point. Some states will register the car and give you plates (with no title), other states wont give you plates until you have the car titled in that state. This is not a big deal - just keep driving on your old plates, but be sure not to let them expire! Work with the clerk at the DMV/BMV if your previous plates are close to their expiration and the state wont issue you new plates due to not having the original title, they should know what to do.

If you are moving TO a title-holding state from one that is not, then the new state will keep your title as soon as its transferred. They will issue you a receipt indicating that you own the vehicle, with a state seal on it - but this is only good as proof of ownership, you can't use it to sell your car. This is called a memorandum title in Ohio. You get the original title back when the lien is removed (you pay off your loan).