Recent purchase inherited a overly simplified lease

[Sam Leon]

My recent purchase of a triplex came with three tenants, and they all have leases expiring in May, August and October 2015.  The lease is a one page lease mostly focused on how much rent and little other details.

Now one of the tenants on a 2/1 has a roommate who I found out is her dad.  She told me her dad is looking for a place and will be staying with her until whenever...its been a month.  Now she lives alone in 2/1 so I am not against an extra as long as I can screen and put on the lease.

My own standard lease has the language to give me final say to allow additional occupants, but this lease doesn't.

So do I have the right to demand her dad to be screened and collect an app fee if the lease has no provision for this?

The current lease has no language on pets either so I worry someone would bring in a 100 pound pit bull and claim ts allowed by the lease.

Thoughts?

Can I insist on screening the extra person?