In the case of most states, this answer would be a simple yes or no. However, with New York, the situation is somewhat more complicated. New York has not banned or abolished the death penalty. However, it has no law about the death penalty that has been declared constitutional and it has no equipment for carrying out the death penalty. No prisoners in New York are currently sentenced to death. The state has not executed anyone since 1963.
After the Supreme Court of the United States temporarily struck down the death penalty in 1972, the New York legislature rewrote its laws to limit the number of cases in which the death penalty could be applied. Those laws were struck down by New York’s supreme court. The last such law was struck down in 1984.
In 1995, Governor George Pataki got legislation through the legislature reinstating the death penalty. However, that law was also struck down in 2004. In 2008, Governor David Paterson ordered all death penalty equipment to be removed from state facilities.
Thus, New York does not have any law banning the death penalty, but neither does it have any law allowing it. Therefore, capital punishment is de facto banned in New York.