IIRC NYC has a "fire code" that the Fire Chief Marshall King Puhba whoever that an occupant cannot have more than 200 rounds of ammunition in their abode. Not sure if he needs a warrant to enforce this "safety code" but I'll bet that the communist NYC probably wouldn't.
It's a myth. It comes from the fire code for dealers. If you are a dealer you need a permit if you are storing more than 200rds for sale. It does not apply to individuals living in their home.
<- Former NYer.