It's a question that I find myself fielding from clients above all others nowadays. The short answer: Who knows. I regularly practice in the housing courts throughout New York City and have furiously been staying on top of the updates but between the latest COVID-19 Emergency Eviction and Foreclosure Prevention Act of 2020 and the Executive Orders, Administrative Orders, Memoranda from Chief Administrative Judges, Directives and Procedures coming out of the civil court, it's hard for even the most experienced lawyers to keep up.
But I will say that it's a little more nuanced than “there's a moratorium on evictions until May 1, 2021,” which is what I hear from tenants everyday, about ten times a day. I'll say it louder for people in the back: “HOUSING COURTS ARE OPEN!” In fact, they are accepting new cases, even ones for non-payment of rent. Cue the shock and horror that landlords should try to collect rent they are contractually entitled to.
At any rate, yes, you can still start a holdover or non-payment case. All you have to do is serve a hardship declaration along with a list of legal providers to the tenant and sign an affidavit indicating that you haven't received it back from the tenant. (Of course, if you are a client of ours, you know we take care of this for you). If of course, the tenant does sign and return the hardship form, then yes, you have to wait and will have to re-serve your predicate notices. The one exception are nuisance cases. Nuisance holdovers are proceeding in the normal course.
The important take away is that whether you file a new case or have a pending case, if the tenant fails to submit the hardship declaration, you can proceed with your case. Now, what “proceed” means will depend on what county you are in. But that's an article for another day.