There are several ways to document and prove unauthorized occupants:
(1) Are they receiving mail in the occupants name at the residence? Verify this by checking with the mailman or the post office;
(2) Is the occupant's car frequently parked at the residence for long periods? (Dated & timed photos of the car at the residence;
(3) Is the occupant seen coming and going to the unit when the tenants are not home? He has his own key. Document this with a log of dates/times of coming and going;
(4) Check with utility companies for any utility bills in his name, or for a sudden increase in utility usage;
(5) Obtain statements from neighbors or other tenants in the building.
(6) Give notice of an annual inspection. Go in and inspect the entire unit, checking all systems for issues with water leaks, electrical, plumbing, heating, smoke detector batteries - a complete inspection. You will need to open closets and cabinets to do this (but not drawers or doors of their personal furniture). Look for signs that the occupant lives there (e.g., gender-opposite items if the person is not the same gender as the authorized tenant, shoe/clothing sizes that would not fit the tenant, etc.)
(7) Check common areas for signs of the extra occupant, e.g., shoes left outside the door, clothing left hanging to drip dry in the laundry, etc.
If it continues despite warnings and you want to document these items, it would be hard for a judge to ignore your logs of dates and times, statements from neighbors, photos of the car, inspection reports, utility statements, and the US postal service delivery.
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I agree with the previous answer and written notice to inspect is good . If your lease states one person, and he claims claim that is true, perhaps a sworn statement signed by your tenant that he is the only party who be a place to start.
You could have a local lawyer look at your lease and have draw up a statement for your tenant to sign. That may let them know you are going to take legal action and are gathering the evidence to hold your tenant to the terms of the lease.
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