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You have the leverage here. She had no legal right to apply her deposit to pay her rent. The security deposit
is to protect you from both unpaid rent and damages
she may have caused to the property. So, by applying the deposit to her rent, she actually is in default. So, it's up to you whether you want to allow her to extend her stay. If she did not leave on June 1, then she does owe you for June and she must pay you. If she does not, then you can file suit against her for the rent AND you can give her a 3-Day Notice to Quit meaning she has 3 days to leave or face formal eviction
. Then, if she does not leave, you would then file your petition for an eviction order and once the court issues that, you can have the sheriff force her out. Since she's month to month, you don't need to issue any letter, you can simply accept her rent and if at any time you want to terminate, you simply need to give her written notice of that at least 15 days prior to the end of the any monthly rental period.
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