I do not know what state you reside in, but it is unlikely that the law requires your landlord to provide a reference for you. Certainly, in Pennsylvania this is not the case. There are a few measures you can take, though, to demonstrate your ability to be a good tenant. First, you can provide copies of receipts or cancelled checks to show that you pay rent promptly each month. Second, you can provide photographs of your present apartment to show that you are able to take good care of a rental unit and that the rental unit you are presently in has no damage.
If you paid a security deposit, and the present landlord refuses to return that money when you leave, most states do have laws that allow you to sue for the return of the security deposit if you have met certain conditions. These conditions often include owing no back rent, leaving the premises in good conditions, providing notice that you leaving, and returning all keys.