Where can you do a background/credit check to apply for rentals?

[Bryan T.]

Is there a site where can you do a background/credit check to show to landlords that they trust to apply for rentals? Let's say you are interested in several rentals but are moving from out of state or are doing a month-to-month lease where you may be renting in multiple locations in a short period of time. 

Is there a site where you can just do ONE background/credit check and show it to landlords instead of having them do a separate background/credit check each time?

Thank you. This forum is extremely helpful as I will be a not only a future renter but landlord/investor/house hacker.