Evicting a month-to-month tenant in New York without a lease

[Frank Mirando]

Hey I'm hoping to get some feedback from those with more experience landlording than me.

I purchased a 2 family house hack situation 5 years ago.  I live in one unit and we inherited the tenant in unit 2.  Upon purchase the tenant refused to sign a lease but agreed to stay month to month and planned on moving to Florida within 2 years.  She has paid rent on time and has not been too much trouble...that is until a tree branch fell on her Jeep Cherokee ( late model not worth more than 3-5k).  Since this incident she has held rent hostage to cover her deductible.  After not wanting to fight, I told her to deduct the 500 deductible from this months rent and that she will have to leave by the end of March and she agreed. 

Since this is not the first time she as said she was leaving , we wrote up a notice to vacate as of March 31st and handed it to her before the end of December 2018.  She seemed ok with it, until I went to collect rent today and she's claiming she cannot find the letter and that since we spelled her name wrong she doesn't know who that person is.  She did promise to leave by the end of March again claiming...she is a woman of her word. 

Tomorrow I will be sending the notice certified mail, however I am not sure how to proceed with this eviction.  Any help from you guys would be greatly appreciated!