The worker was identified as Kevin Kelly, 25, who lived in the Queens borough.
The Buildings Department said 25 violations warranting penalties had been issued since construction on the building began last year, though none involved the safety strap that was cited as the possible cause of the worker's fall Monday.
The department halted work at the site and was reviewing how the straps were used there.
Colleen Rugg, a spokeswoman for general contractor Hunter Roberts, said "Our hearts go out to the family affected by this tragedy."
The building at East 67th Street near First Avenue is about two blocks from a building where two window washers plunged 47 stories in December. One died; the other miraculously survived.