Inherited Tenant with no Lease, can I ask for a security deposit?

[Kelsey Rhea]

My husband and I are in the process of purchasing a duplex where one unit has a tenant who has been there for the entire 17 years the seller has owned the property. Her rent has never increased. She pays no utilities, and there is no lease. Obviously, there is a lot to rectify in the situation. When we take possession, we will be raising her rent and instituting a no smoking policy, which will affect her. We will also have her sign a lease. Can we ask for a deposit should she agree to sign the lease?