While your question is a little unclear, I presume you mean you bought a car and have an outstanding loan on it. That's why the Bank wants to be on the title, either as primary owner or as a lienor, which proves that they have a lien upon the car so that if you sell it before the loan is paid off, they are certain to get paid or the next purchaser "inherets" the lien with the car. It is quite normal and legal for a Bank to insist that they get their name on that title since you apparently live in a Title state in which the title to the vehicle resides in the physical Title document. That means there is no central clearing house for the lien to be filed in by the Bank, so they have no other choice but to insist upon you turning over the Title to them so they can post a lien on it to give notice to any subsequent purchaser that their lien most be satisified before a clean Title can be transferred.
I believe they can sue you to force you to turn the Title over so they can place their lien on it. My suggestion is, if you owe money to the Bank, you let them place a lien upon the Title. Its the fair and right thing to do.
Theodore is right. Ohio is a "strict title" state, which means that if your name is not on the title then you don't own the vehicle. And if the bank's lien is not on the title, then they have no lien at all. That's why the bank is nervous. And Theodore is right that they may sue you sooner or later. If you took out a loan on the vehicle, then the bank has a right to a lien on the title and if you interfere with it, you can count on getting sued over it. If you still are not sure what you should do, then you need to talk to a local Consumer Law attorney who deals with this kind of case. Call your local attorney's Bar Association and ask for a referral to a Consumer Law attorney near you or you can go to this web site page for a Free Online 50 State National List of Consumer Law Lawyers (http://www.ohiolemonlaw.com/ocll-site/ocll-locate_local.shtml) and find one near you (lawyers don’t pay to get listed here and most of them are members of the only national association for Consumer Law lawyers, NACA.net). But act quickly because for every legal right you have, there is only a limited amount of time to actually file a lawsuit in court or your rights expire (it's called the statute of limitations), so don't waste your time getting to a Consumer Law attorney and finding out what your rights are. If this answer was helpful, please check the box below.