The last time I rented, the only thing the landlord asked for was my SSN to run a basic credit report and criminal background check. She gave all the information to me the day I signed the lease agreement which contained a paragraph regarding this information being secured during processing and returned in full.
I would NOT (having working in the collection industry and ID theft anaylist for years) EVER give that information to anyone without something in writing stating the information is secured and will not be misused.