Hollywood film director Woody Allen has rebutted renewed allegations of sexual abuse levelled at him in the new HBO documentary, Allen v Farrow.

Allen and his wife, Soon-Yi Previn, deny claims that he sexually assaulted his daughter Dylan in 1992, calling the series “a hatchet job riddled with falsehoods”.

Previn is the adopted daughter of Mia Farrow, and became involved with Woody Allen in the early '90s. In 1992, Mia Farrow learned of the relationship while Previn was a first-year college student.

In a statement to the Hollywood Reporter, the couple said that film-makers Amy Ziering and Kirby Dick had “spent years surreptitiously collaborating with the Farrows and their enablers to put together a hatchet job riddled with falsehoods”.

“As has been known for decades, these allegations are categorically false," they added.

"Multiple agencies investigated them at the time and found that, whatever Dylan Farrow may have been led to believe, absolutely no abuse had ever taken place.”

Allen v Farrow aired its first of four episodes on Sunday on HBO, and is described as an investigation into allegations which emerged during the custody battle following Allen’s separation from Mia Farrow in 1992.

Episode 1 saw interviews with family and friends who said that even before August 4, 1992 — the day that Dylan Farrow says her father assaulted her — they witnessed behaviour from Woody Allen toward his daughter that they saw as inappropriate.

Ziering made sure to deny that their film was “a collaboration...with Dylan Farrow or the family”.

The Farrows have so far offered no response regarding Allen and Previn's comments on the documentary.

Allegations of sexual abuse against Dylan Farrow were investigated in 1992-93 by Connecticut state police, the Child Sexual Abuse Clinic of Yale New Haven Hospital, and the New York Department of Social Services; none could conclude with the utmost certainty that sexual assault had taken place.

In later episodes, the series raises questions about one of those investigations. A report issued by the Yale Child Sexual Abuse Clinic, at the Yale-New Haven Hospital, found Dylan uncredible after interviewing the child nine times during a seven-month period. According to the series, all the contemporaneous interview notes from those sessions were destroyed when the final report was issued.

Prosecutors in Connecticut declined to prosecute Allen in 1993, but the state’s attorney said that he did so to spare Dylan the trauma of a trial but believed she had been molested.

Mia Farrow and her son - New York Times investigative reporter Ronan Farrow - appear in Allen v Farrow. Allen and Previn declined to participate.

The statement says Allen and Previn “were approached less than two months ago and given only a matter of days ‘to respond’. Of course, they declined to do so.”

Dylan’s brother Moses, who has defended Allen from the allegations, also reportedly declined to appear in the film.

Ziering and Dick have previously worked together on hard-hitting, ground-breaking documentaries about sexual abuse. The Invisible War, which focused on rape in the US military, was Oscar-nominated and The Hunting Ground focused on sex assaults on university campuses.