Would you declose your bank account information and SSCard to a potential landlord?

I am relocating and trying to find a nice townhome or condo to rent. On a couple of applications they are asking for my bank account information checking and savings as well as a copy of my social security card. I don't mind showing it to them but to give them a copy, I am very uncomfortable in doing this. They cound approve me or not approve me and then they will have access to my bank account and social security number.