Two of the women interviewed, Michelle Manning Barish and Tanya Selvaratnam, said Mr. Schneiderman choked and repeatedly hit them. Both women said they sought medical treatment. Mr. Schneiderman also threatened to kill them if they broke up with him, they said, and he told one woman he could have her followed and her phones tapped. All four women who spoke to the magazine said that they had been romantically involved with Mr. Schneiderman, but that the violence was not consensual.

Mr. Cuomo made it clear on Tuesday he wanted someone other than Mr. Vance to investigate the allegations. In March, Mr. Cuomo had directed Mr. Schneiderman to review how the Manhattan district attorney’s office and the New York Police Department handle sexual assault complaints, including a 2015 sexual assault allegation against Mr. Weinstein.

At the time, Mr. Vance had said that there was not enough evidence to prosecute, even though Mr. Weinstein’s accuser, Ambra Battilana, an Italian model, had provided police with a recording of him apologizing in response to a question about why he had groped her breasts

“I want to make sure the district attorneys have no conflicts whatsoever with the attorney general’s office, either institutionally or personally,” Mr. Cuomo said during an unrelated news conference on Tuesday. “So, it’s very important that the district attorney or attorneys that do the investigation have not even the whiff or perception of conflict, because the statement we need to make is you come forward, you show the bravery to come forward, you will be heard, justice will be done.”

In a letter to the acting attorney general, Mr. Cuomo said Ms. Singas would not only investigate the allegations in The New Yorker article but would also look into whether the attorney general’s staff and office resources were used to “facilitate alleged abusive liaisons.”

Ms. Singas was the former head of the special victims bureau in the Nassau County district attorney’s office before she was elected to lead the office in 2015.

The case involving Mr. Schneiderman would normally fall under at least two jurisdictions: One woman said she was physically assaulted in Mr. Schneiderman’s Upper West Side home in Manhattan, and another woman said she was assaulted at a place he was staying in the Hamptons in Suffolk County.