The girl and her mother had arrived at their house and were unloading their vehicle when the tree fell. The third tornado, an EF0 with winds of 85 miles per hour, struck in Newburgh in Orange County. Both are in Putnam County.
Thousands of utility workers were working feverishly to restore power.
Cuomo, a Democrat, said there could be federal assistance, depending on the extent of the damage.
The National Weather Service is investigating whether any tornadoes occurred Tuesday.
Almost 500,000 customers in New York, New Jersey, Connecticut, Pennsylvania, and Virginia were without power by late Tuesday night, fewer power outages than earlier Tuesday, tracking service PowerOutage.us said. Access to the area was restricted due to numerous fallen trees and downed power lines.More news: OnePlus' Bullets Wireless headphones are here to take on Google's Pixel Buds
Known as a meteotsunami, it resulted in fluctuating water levels for several hours Tuesday.
There were more than 100 reports of hail in states including Ohio, Pennsylvania, New York and CT, the National Weather Service said. Most meteotsunamis are too small to notice.
Falling trees killed an 11-year-old girl and a woman in incidents in Newburgh, New York, police said.
A violent spring storm that killed at least five people in the North-eastern United States downed trees and power lines, leaving hundreds of thousands of people without power yesterday.
At Grand Central Station in NY, line service for Hudson, Harlem, and New Haven were suspended due to the storms, the station's Twitter feed said. Two other people were killed in CT in separate incidents when trees fell on their vehicles, local media reported.More news: Man Utd, Arsenal men among best stars to miss out
The storms downed trees and power lines across the region.
Lightning strikes from the storms causes several fires in New Jersey and Massachusetts, AP said.
The National Weather Service said the strong thunderstorms created a small weather-generated tsunami off the New Jersey coast. But there were no reports of damage from the abnormally high tides reported in areas from Perth Amboy in New Jersey to Delaware's Fenwick Island.
Schools in Brookfield, Danbury and other towns announced they would be closed on Wednesday due to storm damage.
Most air traffic was back to normal yesterday morning after more than 500 flights were cancelled at the three major airports serving the NY area on Tuesday, and more than 100 at Boston's Logan International, according to tracking service FlightAware.com.More news: Kia to launch diesel mild hybrid Sportage SUV later this year