if you are concerned with potential fraud or stealing your personal information - why don't you simply call them? You must have the new company's phone number in case of any issues. Give them a call and ask them if they did indeed request this information and then ask them why? If you don't want to give it to them explain why you don't ...
But you could find yourself losing your lease the next time it is up for renewal if you are not so cooperative.
And if you find they did not request this - you could be helping fellow renters by letting the leasing company know so they can inform all their tenants about potential fraud.