Bevon Bloise, a registered nurse at Mount Sinai West, complained on Facebook that the hospital does not have sufficient personal protective equipment, or P.P.E. “I’m also very angry with the Mount Sinai Health System for not protecting him. We do not have enough PPE, we do not have the correct PPE, and we do not have the appropriate staffing to handle this pandemic. And I do not appreciate representatives of this health system saying otherwise on the news.”

“We lost a great fighter during this war,” a co-worker named Diana Torres said on Facebook. She posted a photo of co-workers tying bandannas over their faces in an effort to protect themselves. “NO THIS IS NOT PROPER PPE,” she wrote.

On its Facebook page, Mount Sinai West said it was “deeply saddened by the passing of a beloved member of our nursing staff,” without naming Mr. Kelly.

In an email, a hospital spokeswoman, Lucia Lee, disputed the claim that the hospital had not furnished protective equipment to its staff. “This crisis is straining the resources of all New York area hospitals, and while we do — and have had — enough protective equipment for our staff, we will all need more in the weeks ahead,” Ms. Lee said in the statement.

The New York Post article included a photo of hospital staff wearing garbage bags over what appeared to be scrubs. Two nurses, who spoke on condition of anonymity for fear of being fired, said they were disposable scrubs made of permeable material, which is why nurses wrapped plastic garbage bags around them.

The photo, they said, was taken on March 17, at a time when there were many coronavirus patients at the hospital and others who had yet to be tested but who presented symptoms of infection.

In the emailed statement, Ms. Lee added that “the troubling photo circulating in the media specifically shows the nurses in proper P.P.E. underneath garbage bags.”