Don’t die in the Big Apple: A cheating scandal threatens to cripple New York City funeral homes.

The president of a Manhattan-based undertaking school stands accused of running a scheme to glean the questions on ​a ​national ​board exam — and share them with hundreds of students.

Last week, the state Health Department charged that seven teachers at the American Academy McAllister Institute — dubbed the Harvard of mortuary schools — “engaged in a widespread conspiracy” to game the exam, officials told The Post.

State officials would not name the teachers, but they include AAMI’s president and CEO, Mary Margaret “Meg” Dunn​, The Post learned.​

In addition, more than 300 AAMI graduates ​in 15 states have had their passing scores invalidated by the International Conference of Funeral Service Examining Boards for allegedly sending or receiving emails revealing test secrets​​, officials said. The conference creates and administers the exam.

The state Bureau of Funeral Directing has notified 94 New York morticians that they ​will lose their license​s if they don’t re-take and pass the exam by June 30, or apply for an extension to Dec. 31.

​The crackdown may cause a staffing crisis at local mortuaries, and make it difficult for New Yorkers to make arrangements for loved ones.

“The industry is already short-staffed by 30 percent. This action will only compound the problem,” said Robert Ruggiero, executive director of the Metropolitan Funeral Directors Association. “There’s a limited number of funeral directors already straining to accommodate the public caseload.​”

Ruggiero called it a “witch hunt” ​in which the accused have not been shown evidence of their alleged wrongdoing​, and been denied due process.

Many have been in ​the ​funeral ​business for years​ with​ unblemished records, and fear losing their livelihoods.

“I’m nauseous and losing sleep over it,” said ​a ​city funeral director who graduated from AAMI five years ago.

The cheating accusations center on ​Dunn. A mortician’s daughter, she was briefly married in the 1990s to Joseph Nicelli, a funeral director sent to prison in 2009 in the multimillion-dollar “body-snatchers” scandal, where parts of cadavers were pilfered and sold.

Dunn did not return message​s. A ​spokeswoman said the school would not comment.

An investigation ​was triggered in 2013 when an anonymous AAMI graduate sent a letter to the examining board conference, saying she had received many emails and other materials from Dunn with “very specific and direct answers to the National Board Exam,” court records show.

Soon after taking the exam, the student received another email that Dunn sent to students describing items that “appeared to be taken directly from the test I had just taken,” she wrote, adding: “Ms. Dunn coyly referred to these as her ‘visions.’”

Other AAMI grads have since accused Dunn of forcing them to report to her what was on ​the test, so she could coach others.

For instance, one email, obtained in a court-ordered search of AAMI computers, said test​ subjects focused on “house removals” and “cremains.” It ​quoted the questions and multiple-choice options — then advised ​how to answer: “Obviously, they were looking for A,” ​it concluded.

“I’ve been here 20 years, and we’ve never seen ..​. a scheme of this magnitude,” said Dalene Paull, the conference’s executive director.

The alleged cheating helps explain AAMI’s historically high passing rate, the conference contends. In 2013, 92 percent of AAMI grads passed the science section, compared to 76 percent of peers trained elsewhere.

The conference sued AAMI in Manhattan federal court for ​violating ​t​he test’s security, giving ​its students an unfair advantage, and ​flouting public health and ​welfare law.

Under a confidential settlement in 2014, AAMI paid the conference $1.2 million, the newsletter Funeral Insider reported.

Funeral home trade groups defend AAMI and its graduates.

“The school has done nothing wrong in comparison to ​any ​other educational institution,” Ruggiero said. “​Ev​en the NYC school system​ teaches to the test.”

​​Becoming a licensed funeral director requires an associate’s degree in mortuary science​. At AAMI, it typically takes 18 months​,​ and ​costs roughly $4​,000 to $5​,​00​0 per semester in tuition. Graduates then take the boa​r​d exam​, complete a 12-month apprenticeship in a funeral home, ​an​d​ pass a state test on funeral law.