After learning that a teacher in their Bronx school building was sick with the coronavirus, faculty members were told they could be terminated for warning students to stay away, The Post has learned.

“Staff can get fired for telling kids not to come to school,” a supervisor advised, according to a report of a March 15 teleconference with worried teachers at the Grace Dodge campus in Crotona, which houses three schools.

“Very few students will be in tomorrow. It’s not worth risking your job to lower the number,” the supervisor said.

Later that day, Mayor Bill de Blasio finally announced the city would close schools for students, but require all teachers come in for three days of training on remote instruction.

The report, obtained by The Post, raises troubling questions about whether City Hall and the Department of Education failed to fully safeguard staff and students, and tried to limit information released to the public.

A spokeswoman for Anastasia Coleman, the city’s Special Commissioner of Investigation for city schools, confirmed Friday there is an “open investigation” of the DOE’s response to COVID-19 cases.

The SCI received a letter from Queens Councilman Robert Holden calling for a probe after Brooklyn principal Dezann Romain, 36, died Monday of complications from the virus.

Holden also cited a Post report that the DOE kept Brooklyn Technical HS open for 350 staffers while five ailing teachers tested positive.

“I believe this conduct by the Chancellor to be extremely negligent and irresponsible,” Holden states.

The Bronx report reveals that the DOE delayed closing schools when teachers reported their COVID-19 test results, saying they had to wait until the Health Department ordered it.

“The policy is, if there is no case on DOH record, then it doesn’t exist,” the report says. “If there’s no record, then it is Business as Usual. Therefore, we are open tomorrow.”

That meant the three schools on Crotona Avenue opened their doors for teachers March 17 to 19, and for students to pick up laptops.

In the March 15 teleconference, teachers learned the “city has gotten increasingly tight” about informing school communities about COVID-19 cases.

“We are not allowed to communicate with students and families unless they are vetted by [superintendent’s] office,” the report says.

The Crotona International HS teacher who tested positive on March 12 told The Post he notified his principal immediately, and sent her his lab results from Montefiore Medical Center. He also warned as many colleagues as he could.

Fighting his illness and frustrated that the school remained open for staff training, he called the state and city health departments, as well as 311, but only got “a runaround.”

“It’s been 16 days, and no one from the DOH has contacted me,” he said. “I’m not saying Mr. Carranza has to call me directly, but no one from the DOE had the decency to ask ‘How is this guy doing?’”

As the deadly virus spread, Chancellor Richard Carranza sent a March 10 email telling subordinates not to alert health officials about COVID-19 cases, as The Post reported.

“At the moment, there is no reason for any school to call [the Health Department] to report potential or confirmed cases,” the email said, adding that the DOH would get test results from labs and that school personnel should help “by keeping their phones clear.”

On March 16, identical form letters signed by Carranza were sent to staff members in the Crotona building, saying the Health Department had “confirmed a positive result of COVID-19 in your school community.”

It added, “Based on the confirmed finding, our school building was disinfected” by the DOE’s facilities division.

The letters infuriated teachers who were told to still show up that week. At least a dozen had already obtained letters from their doctors recommending a 14-day quarantine because of their exposure to the teacher who tested positive. Many called in sick.

City Councilman Mark Treyger, education committee chairman, denounced the mayor’s handling of the crisis.

“This is another painful example of how the mayor’s structure for reporting COVID-19 cases is irresponsible, disconnected and broken,” he said. “When a member of the school community forwards a confirmed test result, we should take steps immediately to protect the well-being of the students and other staff in the building.”

Treyger believes the system was set up to avoid liability because Carranza’s memos “are the type not written by a compassionate educator, but a heartless lawyer.”

City Hall spokeswoman Jane Meyer rebutted Treyger: “That claim is false – the health and safety of our students and staff have been the sole driver of every decision made by the Mayor and Chancellor,” she said.

DOE spokeswoman Danielle Filson said, “We immediately looked into this when it was brought to our attention, and when we received confirmation from the state Health Department, we sent notification out to the school community. We encouraged schools and staff to share accurate, confirmed information during this crisis.”

She did not specify when the DOE heard from the state.