New York does have an estate tax which is calculated separately from the Federal Inheritance tax. A federal inheritance may not be due but a New York Estate tax could be due.
In general the New York Estate tax is due on estates greater than $1,000,000.
As the person inheriting money, property from an estate, there is not tax due either federal or State depending on the type of assets received.
Cash, property, stocks, bonds, are not taxable to the heir on an estate. Previously non-taxed assets such as IRA, 401k, US savings bonds would have taxes due to the heir of an estate.