It’s the Harvard of mortuary colleges but now a New York City funeral service school is suing City Hall, accusing it of reneging, since last June, on a deal to send it unclaimed cadavers.

Without the bodies, the American Academy McAllister Institute of Funeral Service says court papers, its national accreditation is at risk.

The city Law department had no immediate comment on the suit against municipal health officials that was filed in Manhattan civil court late last week.

McAllister officials note that things have been much more difficult since Hurricane Sandy flooded Bellevue Hospital’s basement, wiping out the work space they had near the head city coroner.

“Dead bodies or cadavers are as vital to a mortuary school offering a degree as computers are to a school offering an IT degree,” school President Mary Margaret Dunn says in court documents.

Dead bodies are apparently the family business. 

Dunn’s ex-hubby, Joseph Nicelli, a funeral parlor boss, was in a ring of so-called body snatchers caught illegally selling bone and tissue from corpses -- the late Masterpiece Theater Host Alistair Cooke’s body included -- that passed through area funeral homes.

Now 59, he was sentenced to 24 years in 2009 after pleading guilty to enterprise corruption.

McAllister has more than 450 students, who must conduct 10 or more embalmings in order to graduate. (That’s a lot of bodies.)

The school trains many of the directors who run metro New York’s funeral homes and mortuaries.