Yes, you can rent an apartment with no rental history. But you're going to have to provide the paperwork that proves you can afford it.What are ways to get approved with no rental history? You'll provide proof of income, previous rental history and various references. Getting approved isn't always easy. • Fill out the move-out checklist in the back of this booklet when you move out. You will then have the move-out checklist to compare to your move-in. Yes you can fill out without having prior rental history. Once fees are paid, the City will issue the Certificate of Rental Registration. Rental Applications: Every landlord should request a rental application from a potential tenant.