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In eviction process you must first give them notice to vacate. Since they have established residency you will need to give them a 3-7 day notice to vacate. Generally 7 days is recommended but you can by law give them 3 days.
If they have failed to leave within the noted time you will need to go to the local clerk of courts office and file for a eviction. You can pick the forms up at your local law library or purchase them on line. Fill them out and submit them to the clerk of courts office. The clerk will set up a hearing at which time you can request a eviction based on not wishing to renew the lease. The judge will then give them a set time to be out. Generally this is 3-7 days but depending on the situation (Young children, winter, etc) the judge can allow them another 30 days.
If they are not out by the set date the judge orders you can then take the order to your local sheriffs office who can set them out of the home.
I wish you the best,
They are not required to sign the notice.........you can send it to them certified mail or deliver it to them in person as long as they get it. Often in these cases some people choose to hire someone such as the sheriffs office to deliver the notice to vacate so they have proof of the person getting the notice.