By Eric Levenson and Sophie Tatum, CNN

(CNN) -- Prosecutors in multiple jurisdictions will investigate the assault allegations that led to the resignation of New York Attorney General Eric Schneiderman, authorities said Tuesday.

One day after a stunning story in The New Yorker detailed four women's allegations that Schneiderman violently assaulted them, Gov. Andrew Cuomo and law enforcement officials in Manhattan and suburban Long Island announced plans to look into the claims.

Schneiderman "strongly contests" the allegations.

On Tuesday night, Cuomo announced a special prosecutor to investigate the allegations against Schneiderman. Nassau County District Attorney Madeline Singas will serve as special prosecutor and special deputy attorney general, according to Cuomo.

Separately, Chief of Detectives Dermot Shea has discussed an "investigative game plan" with Manhattan District Attorney Cy Vance and detectives will contact the women behind the "very serious allegations," NYPD Commissioner James P. O'Neill told reporters. And the Suffolk County District Attorney's Office has also opened an investigation, spokeswoman Sheila Kelly said.

Vance objected to the governor's decision to appoint a special prosecutor in a letter to Cuomo Tuesday.

In it, he said Cuomo has "intruded further into the criminal process by 're-assigning' the Schneiderman matter away from my office to a different elected prosecutor."

While voicing confidence in Singas, he criticized the governor's decision to supersede the Manhattan DA's office in the Schneiderman investigation with the special prosecutor, saying that the "charging and jurisdictional decision making should be left to independent prosecutors who are answerable to their local constituents."

Counsel to the governor, Alphonso David responded to Vance's criticism calling it "inappropriate and misguided" and said in a statement that the action was taken "to ensure both the integrity of the investigation and the public's confidence in the process."

New York Solicitor General Barbara Underwood was named acting attorney general.

"I am honored to serve the people of New York as acting Attorney General," Underwood said in a written statement. "The work of this office is critically important. Our office has never been stronger, and this extraordinarily talented, dedicated, and tireless team of public servants will ensure that our work continues without interruption."

Two of the women alleging they were assaulted by Schneiderman are Michelle Manning Barish and Tanya Selvaratnam, who spoke on the record to the magazine.

They said they had been romantically involved with Schneiderman and the violence was nonconsensual. The New Yorker described the violence as occurring "often after drinking, frequently in bed and never with their consent."

In one instance, Manning Barish told The New Yorker, Schneiderman hit her and then choked her.

"All of a sudden, he just slapped me, open-handed and with great force, across the face, landing the blow directly onto my ear," Manning Barish said. "It was horrendous. It just came out of nowhere. My ear was ringing. I lost my balance and fell backward onto the bed. I sprang up, but at this point there was very little room between the bed and him.

"I got up to try to shove him back, or take a swing, and he pushed me back down. He then used his body weight to hold me down, and he began to choke me. The choking was very hard. It was really bad. I kicked. In every fiber, I felt I was being beaten by a man."

Schneiderman's stunning resignation ends what had been a promising prospective career in Democratic politics. The attorney general was a frequent critic of President Donald Trump and had been a vocal proponent for women's rights and for the #MeToo movement.

Just hours after The New Yorker story published, he resigned.

"In the last several hours, serious allegations, which I strongly contest, have been made against me," Schneiderman said in a statement. "While these allegations are unrelated to my professional conduct or the operations of the office, they will effectively prevent me from leading the office's work at this critical time. I therefore resign my office, effective at the close of business on May 8, 2018."

Schneiderman called the activity role-play

Schneiderman released a statement Monday on Twitter saying he had engaged in "role-playing."

"In the privacy of intimate relationships, I have engaged in role-playing and other consensual sexual activity," he wrote. "I have not assaulted anyone. I have never engaged in non-consensual sex, which is a line I would not cross."

But on CNN's "New Day" on Tuesday, reporter Ronan Farrow rejected Schneiderman's claim that the alleged violence was a form of sexual role-play.

"This was not role-playing. This was not 'Fifty Shades of Grey.' It wasn't in a gray area at all," Farrow said. "This was activity that happened, in many cases, fully clothed, outside of a sexual context during arguments."

Cuomo, also a Democrat, was one of several political allies who called on Schneiderman to resign. On Tuesday, the governor said the allegations were "shocking" and "disturbing" and praised the courage of the women who came forward.

"I think the article was graphic and definitive in the reporting of the statements, the actions, the behavior, the corroboration. I thought it was a very powerful and damning set of facts," he said.

Schneiderman's ex-wife, Jennifer Cunningham, came to his defense Monday evening, saying that the allegations "are completely inconsistent with the man I know."

"I've known Eric for nearly 35 years as a husband, father and friend. These allegations are completely inconsistent with the man I know, who has always been someone of the highest character, outstanding values and a loving father. I find it impossible to believe these allegations are true," Cunningham said.

Who is Barbara Underwood?

Underwood was appointed solicitor general in 2007 by Cuomo, who said that the person in that role automatically becomes acting attorney general in the event of a vacancy.

Prior to that, Underwood served as counsel and chief assistant to the US Attorney for the Eastern District of New York, according to her online biography, and has argued 20 cases before the US Supreme Court.

Cuomo praised her competency and professionalism.

"She's an extraordinarily competent woman, so I have no fear in the immediate. She will provide good stewardship for the office and she's a total professional," he said.

Underwood will serve as acting attorney general until the state legislature appoints an interim replacement. An election for the position already was set for later this year.

In the short term, though, the attorney general's office will be in fine hands, Cuomo said.

"The only good news here is the solicitor general is a top-quality person who will not be running for office, so she won't be playing politics and she'll just be doing the job," the governor said.