The incident occurred about 9.30 am yesterday, New York time, as he and six others tried to lower a tower crane at a building site on the West Side of Manhattan.
Crane rigger Anthony Esposito, 48, had been on a 6 m platform attached to the crane about 40 floors up when it is believed he lost his footing.
Mr Esposito was wearing a safety harness, but it was not attached to anything, Mayor Michael Bloomberg told The New York Times.
Investigators are now trying to determine whether the platform had been properly anchored to the structure. When complete the 58-storey building will include 1,350 residential units and be known as Silver Towers on the River.
The fatal accident follows two other tower crane incidents earlier this year, which killed a total of nine people.