The family of the woman who accused billionaire investor Leon Black of raping her inside Jeffrey Epstein’s Manhattan mansion two decades ago when she was a teenager has said that they believe the woman is lying — not just about the alleged rape, but also with her claim that she has autism, according to court papers filed by Black’s attorneys.

The woman — only identified in court documents as “Jane Doe” — filed a lawsuit in Manhattan federal court last month alleging she was only 16 years old when Black, then 51, pinned her down inside Epstein’s Upper East Side townhouse in 2002 and abused her with sex toys, causing her to bleed.

Black’s legal team, which has dismissed the claims as an attempt to “smear” his name “with no basis in fact,” claimed to have learned the identity of the woman — who Black claims he has never met — and therefore claimed it had the right to investigate her story, according to papers filed in Manhattan federal court on Monday.

The latest filing, which claims that investigators for Black “spoke with numerous witnesses, including close and extended family members,” alleges that Doe does not, in fact, have autism or Down syndrome but was instead diagnosed with borderline personality disorder.

“Plaintiff became aware of and studied those behaviors and began intentionally displaying them in her twenties in order to present herself as a person with autism,” according to the court documents, which noted that Doe avoided eye contact once she “noted that people with autism don’t look other people in the eye.”

“She had never before displayed [the behavior],” the documents added.

Jeanne Christensen, a partner at Wigdor Law who represents Jane Doe, denied the allegations in Black’s Monday filing.

“Black hopes to shift our attention to defending ourselves against baseless claims so that he can continue to have his private investigators bully and threaten our clients who have dared to call out his sexual violence publicly,” Christensen said in a statement.

According to the documents filed by Black’s attorneys on Monday, Doe’s relatives also reportedly admitted that she “used a series of different names and personas, has a history of making up alternate realities” — a result of her personality disorder diagnosis.

To defend Black against the so-called “uncorroborated allegations” against him, his legal counsel at Perry Law, Quinn Emanuel Urquhart & Sullivan and Estrich Goldin also claimed that Doe recently “posted on social media that she had been abused by Jeffrey Epstein.”

However, according to the documents, “she had never made such allegations before. Her family told her that they did not believe this to be true, and she deleted the posts.”

The unidentified woman claims she was trafficked by Epstein and his longtime gal pal Ghislaine Maxwell after meeting the debauched couple at an “adult party” she attended with her allegedly abusive cheerleading coach at age 15.

However, Doe only “participated in a county cheerleading program when she was a senior in high school — not when she was 15, as alleged,” the latest filing by Black’s attorneys claims.

It also noted that the program “did not involve overnight trips,” and that it was only eligible for high school students. If Doe was a member of the group as a high school senior, she would have been around 18 years old, according to the filing.

The latest court filing was in response to Doe’s motion to proceed anonymously, which was filed in US District Court on Friday accusing Black of stationing “a large SUV outside the plaintiff’s home ‘to harass and intimidate Ms. Doe’” just two days after she filed her lawsuit on July 27.

“It had nothing to do with Mr. Black,” the latest filing insisted, noting that investigators — led by “83-year-old decorated Army veteran” Carlos Melendez — didn’t begin working on Black’s behalf until Aug. 7.

Investigators first spoke with Doe’s father in the early afternoon before making appointments to meet with her mother later that day, according to court documents.

The filing claims the investigators went to lunch before meeting with Doe’s mother, which made them late for the appointment.

“As a gesture of politeness, they brought dessert over and apologized that they ‘made the lady wait,’” according to Black’s lawyers.

However, Doe claimed that her parents received a visit from two men claiming to be fraud investigators from Florida, according to the motion to proceed anonymously, which was obtained by The Post.

They visited “in pathetic fashion” with a cheesecake in hand in the hopes that they’d be invited inside, the filing stated.

Once inside, the July filing alleges that the investigators revealed that they had photos of Doe’s minor child while peppering her parents with questions about Doe’s childhood and medical history.

Doe claimed that her parents, aunt and close friends were contacted by the same investigators, who were reportedly working with the company SIC Inc., according to the filing by Doe’s attorney, Christensen at Wigdor Law.

According to SIC’s website, Melendez founded SIC in 1984.

After responding to Doe’s motion to proceed anonymously, Black filed a lawsuit against Wigdor for filing “three separate headline-grabbing lawsuits which it knew, or should have known, were false.”

The filing marks Black’s second complaint against Wigdor.

Black won a previous legal fight against Wigdor client Guzel Ganieva in May who made similar allegations when a New York state judge dismissed Wigdor’s accusations that Black defamed her by falsely claiming she tried to extort him after accusing him of rape.

“Since Leon just sued us again to deflect from his own hideous conduct I have to deal with this now,” Christensen told The Post.

“This latest attempt by Leon Black to deflect public attention away from his own disgusting conduct by suing lawyers who represent women he has victimized is appalling. We will not be deterred by such obvious tactics and are confident he will be held accountable,” she added.

Doe has still insisted that she attended the party as an underage cheerleader, where Maxwell fawned over her “beautiful bright blue eyes, blonde hair and perfect hair” that made her look like a living “doll,” according to the lawsuit filed in July.

She reportedly met Black one year later, after already visiting Epstein’s infamous Pedophile Island in the US Virgin Islands, his Palm Beach mansion and his Manhattan abode, where she was forced to sexually “massage” the creep, and later, his friends, according to the suit.

“In 2002, at his Manhattan townhouse, 9 East 71st, Jeffrey Epstein executed a ‘hand off’ to his close friend Leon Black,” the filing alleges.

“But what passed directly to Black’s hands from the hands of Jeffrey Epstein was a human being – not a ball.”

The woman alleges Epstein told her that Black was “important” and a “special friend” to him — though the she recalls thinking that the former Apollo CEO now worth $10.1 million looked like an “ogre,” according to the lawsuit.

She claims she was ordered to strip naked and give Black the same massages she gave Epstein. But Black instead allegedly violently picked her up and threw her down on the massage table, the suit states.

“She tried to scream but Black placed his hand over her mouth and leaned over her while ripping off her shirt and under her skirt pulling her underwear off,” the filing reads.

“Plaintiff was crying and terrified. Black asked her repeatedly what made her ‘Jeffrey’s special girl’ and throughout the assault called her demeaning, shameful, disgusting names.”

When the girl tried to fight back, Black allegedly threw her onto the floor and slammed her against the walls, the suit claims.

Epstein found her crying on the floor, but refused to take her to the doctor, instead claiming Maxwell would “take care of her” — only to then put her on a plane home, the filing states.