Richard, 65, was the only one aboard the Piper PA-46- 500TP Meridian aircraft when it crashed on Friday less than a mile from takeoff at an airport near White Plains, airport manager Peter Scherrer said after the crash.
He said the plane disappeared from radar and authorities lost contact with the pilot.
Police were notified that a plane had crashed in the hamlet of Purchase, missing a house by about 200 feet, Scherrer was quoted as saying by CNN.
He was headed to Portland, Maine, after flying into New York on Thursday for his father's 99th birthday, Scherrer said.
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He described Richard as an experienced pilot and said the morning was foggy with a quarter-mile visibility.
"This is a terrible tragedy," the Rockefeller family said in a statement released by spokesman Fraser P. Seitel.
"The family is in shock. Richard was a wonderful and cherished son, brother, husband, father and grandfather. He was an experienced pilot and respected medical doctor. It is just horribly sad."
Officials from the Federal Aviation Administration were at the crash site, and National Transportation Safety Board members were on the way to the scene, said Harrison, New York, Police Chief Anthony Marraccini.