There have been attempts in the past to improve worker safety, but that often simply gave rise to new methods of thwarting regulators. After a spate of crane and scaffolding accidents in 2007 and 2008, the city required workers to obtain photo identification cards testifying to the completion of safety courses approved by the safety administration. But most workers must pay the $300 fee themselves and take time off, usually two days, for training.

As a result, fraudulent cards have proliferated, investigators say; the going rate is now $25 to $80. Mr. Colorado had a fake card, OSHA records show.

As a deterrent, the city’s Investigation Department has conducted random inspections of the cards on construction sites since 2012. This year, more than 20 people have been arrested. During a sweep in early October in northern Manhattan, witnessed by The Times, investigators inspected the OSHA cards of 74 workers. Three fake cards were confiscated, while 10 other workers lacked documentation.

In an unusual move, because criminal liability is often hard to prove in construction accidents, the Manhattan district attorney’s office filed manslaughter and other charges in August against two construction managers and the companies for whom they worked in the death of Carlos Moncayo. Mr. Moncayo, a 22-year-old from Ecuador, was crushed in April at a construction site in the meatpacking district where the former restaurant Pastis will give way to a Restoration Hardware store.

Private inspectors had repeatedly warned the company of treacherous conditions, only to be ignored, prosecutors said.

The accident prompted the Buildings Department to post a new warning, reminding inspectors to call either 911 or the agency’s emergency hotline immediately — not the company — if they noticed any “uncorrected hazardous conditions.”

“Why didn’t we do it this way five years ago?” Mr. Peters, of the Investigation Department, said at a news conference. “Honestly we should have. We didn’t.”