It is currently not clear what caused the crash, but it was reported that there was light snow and fog at the time.
The small plane was flying from Newark airport in New Jersey to Buffalo Niagara International Airport.
Before the crash, there were no concerns by the pilot or the air traffic controller, but suddenly the controller could not contact the plane, and had to request other planes in the area to verify that it was still in the air.
Eyewitnesses spoke of hearing unusual sounds coming from the plane before it crashed.
Dave Bissonette, emergency control director in Clarence, described the crash as a "catastrophic event".
"It's remarkable that it only took one house," he added.
"As devastating as that was, it could have easily wiped out that entire neighbourhood.
"The fuselage of the plane lies directly on the footprint of the house. It basically dove right into the top of the house from my perspective, and again I am no expert on recreations, but it landed on the house," he said.
