Though New York does not have an inheritance tax, there is a state level estate tax in the Empire State. The exclusion is about half of the federal exclusion, so you could be federally exempt and still be exposed to the state estate tax. The maximum rate of this tax is 16%.
The exclusion is far lower, and that’s a positive, but there is also a difference between the two taxes that is negative. If the value of your estate exceeds the amount of the state level exclusion by more than 5%, you cannot use the exclusion. The entirety of your estate would be subject to taxation.