Somewhere in your lease should be the occupancy clause that states who may legally occupy the leased premises.
A good lease might say some language to the effect of "guests may not stay for more than five days without our prior written consent." Check your lease language. If you have to move to evict in a court proceeding, the lease language you have will control the remedy.
Using the written documentation you have is a good place to begin. Contact a local lawyer - many may give you a short free consultation - to discuss your specifics. Far too many variables exist in the short post you wrote for any further observation by me. Many attorneys have information posted here on Avvo.
You might find my Legal Guide helpful "How to Choose A Lawyer For You"
You might find my Legal Guide helpful " What Do I Tell My Lawyer"
No one can know what the record is in the case because online we cannot see your documents. You need a lawyer. Check with a lawyer in your locale to discuss more of the details.
Good luck to you. God bless. Best of luck to you.
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Your guest appears to be guilty of criminal trespass and the police may help as long as you can show this person is not on your lease, you asked the person to leave and they didn't (and you apparently gave notice in writing). Criminal trespass occurs when someone comes on your property accidentally or intentionally or initially has permission but you then revoke permission by notifying them to leave, and they don't. If the police won't help unfortunately you may wind up having to file an eviction lawsuit. The best thing to do would be to talk to a local attorney because there may be more facts that affect the situation.