An interracial couple complained that their posh private school was allowing student segregation — and was socked with trumped-up child-neglect raps because of it, according to a Bronx lawsuit.

Columbia University professors Hilary Hallett and Christopher Brown say a staffer at Ethical Culture Fieldston School anonymously accused them of not feeding their sixth-grade son and ignoring a sports injury.

The couple said the staffer manufactured the raps because they had complained about poor race relations at Fieldston.

Brown and Hallett said Fieldston was allowing “self-segregating” among sixth-grade kids, especially during sporting activities, according to their attorney, Derek Sells.

Their son also questioned a white classmate who made a racially derogatory statement last year and had to apologize to his class. That child’s parents learned of the confrontation and complained to administrators, according to Sells.

Soon after voicing their concerns, the parents said, they were suddenly facing child-abuse raps and were visited by an Administration for Children’s Services investigator at 8:30 p.m. on Nov. 20 of last year, according to the suit.

They “were physically examined, photographed and interrogated by a stranger” and their son was “terrified of being taken away from his parents,” court papers state.

ACS cleared Hallett and Brown of the allegations last November.

“We have been and continue to be shocked and disappointed that the school’s administration has shown no interest in or concern for the damage it has caused and continued to cause our family,” the couple said in a statement Tuesday.

Hallett and Brown initially demanded a $8 million payment from the school to compensate for their ordeal or threatened to sue in court.

But Fieldston administrators rejected the ultimatum and accused the couple of “profiteering.”

“We are saddened that anyone in our community would try to undermine this important system with a baseless lawsuit that puts profiteering ahead of students’ safety,” Head of School Jessica Bagby wrote in a letter to parents last month.

The school leveled a similar money-grab accusation in a statement to The Post on Tuesday.

“Lawyers are now trying to extract an $8 million payout from the school simply because of a claim that an anonymous reporter followed the requirements of the mandatory reporting law that protects children,” they said.

Sells countered that ACS accusations must be “reasonable.”

Claiming libel, racial discrimination and retaliation, the suit seeks unspecified damages.