New York Gov. Andrew Cuomo has appointed a special prosecutor to investigate former New York Attorney General Eric Schneiderman after four women came forward with allegations he physically abused them. Cuomo said late Tuesday that Long Island's Nassau District Attorney Madeline Singas will investigate and possibly prosecute "any and all matters concerning the public allegations" against Schneiderman.

Cuomo said Singas also will investigate whether Schneiderman used his staff or office resources to facilitate the alleged abusive liaisons.

"The integrity of our justice system is of paramount importance. News of Schneiderman's alleged improprieties as the State's chief legal officer are grossly disturbing and must be fully investigated. The brave women who chose to come forward deserve swift and definitive justice in this matter," the governor said in a statement.

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Four women accused the Democrat of physical violence in a New Yorker article. Schneiderman announced his resignation Monday three hours after the article was published, but he has implied his conduct was either welcomed by the women, or was not as they described.

The New Yorker report revealed that Schneiderman "repeatedly hit them, often after drinking, frequently in bed and never with their consent," according to the women.

The women didn't come forward with their allegations at the time, reporters Jane Mayer and Ronan Farrow wrote, and Barish and Selvaratnam sought medical attention for what they claim was "assault." They describe being slapped hard across the ear and face and choked.

The NYPD has told CBS News that they have no complaints on file. The department said Monday if it receives complaints of a crime, it will investigate them thoroughly.

Schneiderman has been an outspoken supporter of the #MeToo movement, filing a lawsuit in February against Hollywood producer Harvey Weinstein and the Weinstein Company over allegations of widespread sexual harassment and misconduct.

Schneiderman launched a civil rights probe into the New York City-based Weinstein Company in October after The New York Times and The New Yorker exposed allegations of sexual assault and harassment spanning decades. The company later fired Weinstein.

Earlier Tuesday, Cuomo pointed out that when the scandal broke, Schneiderman was in the process of investigating why Manhattan District Attorney Cy Vance did not bring sexual harassment charges against Harvey Weinstein, CBS New York reports.

"That is a potential complication," he said, calling for an "independent district attorney, so there is justice."

CBS New York asked Mayor Bill de Blasio and NYPD Commissioner James O'Neill if they were comfortable with Vance's office handling the probe.

"At this time, we are. We're comfortable working with Cy's office to investigate these allegations," O'Neill said.

Schneiderman's resignation went into effect Tuesday at the end of business hours. Under the New York Constitution, a vacancy in the office is filled by the state Legislature.