In New York, there are two main types of proceedings that a landlord can bring against a tenant in Housing Court. The first is a nonpayment proceeding, and the second is a holdover proceeding.
In a nonpayment proceeding, the landlord is suing the tenant for back rent. After making a legally sufficient demand for the back rent, the landlord serves the tenant with a nonpayment petition. Once the case gets in front of a judge, it can either be settled or go to a trial. Generally, the tenant is given a certain amount of time to pay the back rent. If it is paid, the case is dismissed. If not, the tenant is evicted. The tenant also can bring up defenses, such as bad conditions.
In a holdover proceeding, the landlord wants the tenant to vacate the apartment. In general, the landlord must serve a notice on the tenant terminating the tenancy. If the tenant does not move out, the landlord can serve the tenant with a holdover petition. Once in court, the tenant will be given a certain amount of time to move. Again the tenant may have certain defenses.
The existence of a written lease can change the legal requirements and rights in both of these cases. Also, if the apartment is subject to rent regulation or any kind of government subsidy, that can also have an effect. Finally, there were new laws passed in New York in 2019 which changed many of the laws regarding evictions.