The United States of America has four levels of government that make laws: federal, state, county, and municipal.
The federal government and at the present time 31 of the 50 states have death penalties.
Did or do any counties and municipalities have death penalties or the power to decree death penalties for crimes?
The fourteenth amendment to the US Consitution, section 1, says:
Section 1. All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside. No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.
This clearly says that states cannot deprive any person of life without due process of law. It says nothing about counties or municipalities depriving people of life without due process of law, which would have been a strange omission if counties and municipalities had death penalties or could have death penalties.
I strongly suspect that for centuries no county or municipality in the USA has had the authority to enact death penalty legislation.
Therefore the statement that:
If Jumping Off a Building Doesn't Kill You... the City of NYC Will
The penalty for jumping off a building is death.
could only be correct in the sense that courts physically located in the City of New York could apply state or federal laws to sentence someone to death for jumping off a building.
New York State laws and their penalties should be equally applicable everywhere in New York State where it is physically possible to break them. Since there should be buildings in every county and municipality in New York State, any New York law against jumping off of buildings should apply equally in every county and municipality in New York State.
Federal laws and their penalties should apply everywhere within the USA where it is possible to break them. Since there should be buildings in every state, county, and municipality in the USA, any hypothetical federal law against jumping off of buildings should apply equally in every state, county, and municipality in the USA.
Possibly there are restrictions to the law, like only jumping off of buildings that have sidewalks below. But a state law would cover many places in New York State with sidewalks below buildings and a federal law would cover many more places with sidewalks below buildings in all of the states.
Maybe the law prohibits jumping off buildings over a certain height.
The tallest building in New York State outside of New York City is the Erastus Corning Tower in Albany, at 589 feet or 180 meters. At the present time there are 113 buildings in New York City over 600 feet (183 meters) tall, so a state law against jumping off a building over 600 tall would only apply to those 113 buildings.
If there was a federal law against jumping off buildings over a specific height, the only way for it to apply only in New York City or New York State would be for the height limit to be somewhere between 1,451 feet (453 meters), the height of the Willis Tower in Chicago, and 1776 feet (541 meters) the height of One World trade Center in New York City, and it would only apply to one building at the present.
It is easy to believe that jumping off a building could count as an charge of committing reckless endangerment, attempted murder, attempted suicide, etc. If a criminal was planning to commit a crime and the police tried to stop him, jumping off a building could count as resisting arrest or fleeing from custody, and could be a count in the charge of attempting to commit the other crime he was trying to commit.
I don't believe that jumping off a building would be a specific crime in itself with a specific penalty instead of simply being a method of committing another crime.
But the laws can be very strange so there may be a slight possibility that there could be a law in New York City or State specifically against jumping off a building.