You can rent the room. You should have a formal lease. The big concern is how much of the house do they get access to. Living Room? Dining Room? Attic? Garage? There are form leases on line, at stationery stores and through some realtors.
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You should thoroughly check out anyone you are going to have living in your home. You should definitely have a written lease. And if the rent is late, you should move promptly to obtain payment or evict.