I did some searches on past forums and while I found some info, I couldn't find anything that was exactly similar to my scenario.

I purchased a quad-plex this past Nov.  The property was poorly managed and maintained.  All four units have existing tenants that were on verbal month-to-month leases. I had an Estoppel Agreement filled out prior to closing.  None of the tenants had signed a lease for the property, only one had a portion a security deposit. Three of the tenants seem like good tenants that I would like to keep.  However, one seemed like trouble (even when I was under contract).

Bottom line up front: The troublesome tenant is refusing to sign the lease, and is claiming that I am discriminating against her due to her disability (FYI the lease is almost exactly the same lease from @Brandon Turner's book on managing rental properties).  Because she has not signed a lease on the property, and is now refusing to sign my lease I am assuming the law is on my side as the landlord/owner correct?  Does anyone have any advice?  Can I kick her out?  I know that eviction can be a long/expensive process, is this my only option if she doesn't sign?

For some additional background, the property is located in Florida.  She is paying well under market rent, but has paid on time.  I am having all the tenants sign month to month leases until May when I will then have them sign year long leases.  My plan was to keep this troublesome tenant on for the month to month until the summer when I would notify them that their lease would not be re-newed, and find a better tenant in the summer months.  I suspect she has drug related problems, and the police have been called to the property multiple times.

Any advice or help would be greatly appreciated.