You can simply give them a notification to leave the house for the tenure which was mentioned at the time of agreement to rent your house. If still confused then ask the real estate through whom you had rented signed the legal agreement. Hope that it works and if still confused then better consult online from real estate experts at bayut.com/community.
You need to look at the lease the person signed, unless they did not sign a lease. I am not sure specifically about New York, but often if there is no lease, it means it is a month-to-month contract. If that is the case, you could probably give them notice 30 days out.
But as kprimeaux said, if they have a signed lease, you can't just kick them out without them violating the lease in some way. And even then, evicting a resident is quite hard. Often, judges tend to be very pro-tenant, so you must follow all guidelines to the letter when trying to evict.
Hope that helps!
If they are not in violation of your rental agreement, you can't just kick someone out of the lease if they do not want to leave. My advice would be to contact a real estate/eviction attorney in your state. Or just ask them to leave.
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