Have to look at deaths.
Hospitalizations are going down. Deaths not so much yet. The data are for the whole state, not just NYC. The people dying may have been hospitalized for a while before dying, so they may not yet show the effect of reduced numbers of people coming into the hospitals.
Also, the clinical study of the effect of hydroxychloroquine and Z-Pack currently underway in NYC may be having an effect on the number of NYC deaths, but it is not obvious in the data from the whole state.
Here is a linear plot of the number of new Covid-19 Cases in New York (the whole state) versus days since March 5. I added the latest data for April 7. New cases continued to decrease from the high three days earlier.
Here is the link to the new plot:
Hopefully new cases will continue to decline.