If the rental lease ends, do we have to continue to rent to tenants?

Our tenants have been late with the rent several times and they dont follow the apartment rules. They pay the rent a day after te grace period or so. Their lease will end in two months. They hinted that they would like to stay longer. In NY State do we have to rent the apartment to them after their lease end? I... show more Our tenants have been late with the rent several times and they dont follow the apartment rules. They pay the rent a day after te grace period or so. Their lease will end in two months. They hinted that they would like to stay longer. In NY State do we have to rent the apartment to them after their lease end? I prefer not to but my wife says we have to. Legally what is the rigth thing to do?
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