Staten Island resident Thomas Patane was standing on a platform inside the elevator shaft last Thursday when he fell from the fifth floor to the basement.
According to the Department of Buildings (DOB), Patane was wearing a safety harness but had not connected the harness to a lifeline.
A second man fell from the second floor to the first floor after being hit from falling debris, but his safety harness was attached to a lifeline and his injuries appeared to be non-life threatening, the DOB said.
Police received a call at 8:15 a.m. to report the incident. Both men were taken to Elmhurst Hospital, with Patane dying in transit.
Both men were employed by Hudson Elevator Group.
"We are deeply saddened by the loss of our employee and our sincere sympathies go out to his family," the company said in a statement. "At this time, as this tragic accident is under investigation, we cannot comment any further."
They were working on a new, six-floor elementary school at 45-45 42nd St, which is planned to open as P.S. 313 in September.
After the incident, the site was placed under a full stop work order and seven Environmental Control Board (ECB) violations were issued, according to DOB.
Last year, DOB saw three construction-related fatalities, while in 2012 there were eight. Numbers have not yet been published for 2014.