What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?

ONE, I can find ONE event and one only over my entire lifetime that actually did smack the R.E. market down and that took the largest financial event in world history since the Great Depression to do it. 

What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?

What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?

They went around order services that was not authorized. 

She passed all of my screening tests, background check, rental history check, good credit score, 3x monthly income of rent, and all of her references had only glowing things to say about her. 

If the authorities contact you, let them know that you are not the one denying access.As for the lease, you technically can't sign a new lease unless the current one has expired or you have consent from all the Tenants, including the one that left.

What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?

What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?

You now have someone occupying the property that was not screened/approved and you have very little legal authority over them because they are not on the lease.I would tell your legal Tenant to pay the rent and get this guy out in one week or you're going to evict and come after them both, including court and attorney fees.