Findings from the federal Occupational Safety and Health Administration claimed Rapetti Rigging Services neglected to inspect the nylon slings it was using to hoist a huge steel crane component. It said the company was therefore unaware one had been damaged.
OSHA said the failure to notice the cuts and snags in the sling was one of three factors that led to the collapse.
Rapetti is also accused of failing to follow instructions from the manufacturer when raising the crane and not using padding to protect the slings from sharp edges on the crane part, the New York Times has reported.
Two other companies, Reliance Construction Group and Joy Contractors, are also facing fines of £11,000 and £41,000 respectively.
The incident on 15 March was the first of two fatal crane collapses in New York in less than three months.
Seven people – including a crane operator and three riggers – were killed and two dozen were injured.