Washington (CNN) The chairman of the Senate Judiciary Committee announced Tuesday night that panel Republicans have hired outside counsel Rachel Mitchell to question Supreme Court nominee Brett Kavanaugh and the woman who has accused him of sexual assault.

Mitchell, according to a news release from Senate Judiciary Committee Chairman Chuck Grassley, is on leave from her role as deputy county attorney in the Maricopa County Attorney's Office. There, she also is the chief of the special victims division.

"I promised Dr. Ford that I would do everything in my power to avoid a repeat of the 'circus' atmosphere in the hearing room that we saw the week of September 4," Grassley said in his Tuesday night statement. "I've taken this additional step to have questions asked by expert staff counsel to establish the most fair and respectful treatment of the witnesses possible."

The move comes as Kavanaugh's historic hearing, in which he and one of his accusers, Christine Blasey Ford, will testify, approaches on Thursday and parties on both sides clash over whether a second woman's recent allegations of inappropriate sexual behavior by the nominee will also be discussed during the hearing.

Kavanaugh has denied both women's allegations.

"The truth is I've never sexually assaulted anyone in high school or otherwise," Kavanaugh said in a Fox News interview Monday night.

Grassley, R-Iowa, would not disclose as of Tuesday afternoon the identity of the outside counsel out of concern for her safety.

She will ask questions for the GOP senators while Democrats do their own questioning, Grassley said.

Senate Majority Leader Mitch McConnell told reporters on Tuesday afternoon that he did not think men should be "disqualified" from listening to the evidence and making decisions, but pointed to the hiring of the outside counsel, who he referred to as a "female assistant."

"As I said earlier, and I think you already know, we have hired a female assistant to go on staff and to ask these questions in a respectful and professional way," McConnell said. "We want this hearing to be handled very professionally, not a political sideshow like you saw the -- put on by the Democrats when they were questioning Judge Kavanaugh."

The decision by the all-male Republican side of the committee to have its questioning conducted by a female lawyer has come under fire by Democrats, who on Tuesday criticized the Republican side for keeping the lawyer's identity a "mystery."

"Who is going to speak for all of the 11 Republican senators?" Illinois Democratic Sen. Dick Durbin said. "We don't have the name, do we? Someone has been given a new job -- a person we don't know. At some point that secrecy has to be unveiled. We should at least know who is going to take the place of the 11 duly elected senators."

Senate Minority Leader Chuck Schumer, D-New York, said, "No one can find that out. That is a mystery."

Although the sticking points don't seem to be a roadblock that will force a delay of the hearing, there is fierce negotiating going on between lawyers for Ford, who has accused Kavanaugh of sexual assault in the 1980s when they were both teenagers, and the Republican staff on the Senate Judiciary Committee.

All along, lawyers for Ford have objected to the Republicans' plan of using an outside counsel to question their client.

Grassley said the public would "probably not" know the identity of the outside counsel before the hearing and claimed the move would pull politics out of the situation.

"We have done it because we want to depoliticize the whole process like the Democrats politicized the Anita Hill thing," Grassley said. "The whole purpose is to create an environment where it is what Dr. Ford has asked for -- it be professional and not be a circus. That's what we're up to."

Monday night, a lawyer for the committee confirmed in an email to Ford's lawyers that Grassley has hired an "experienced sex-crimes prosecutor" to serve as an investigative staff counsel for the hearing, according to a source on the committee.

Republicans recognize that there are only men on their sides of the aisle.

Sen. Bob Corker, a Tennessee Republican, said Tuesday that if he were on the Judiciary Committee, he wouldn't want to be asking questions.

"Somebody will do something that you guys will run 24/7," he told reporters.

Although Ford had agreed to the hearings, the issue had remained a sticking point, and two of her attorneys contacted the committee Monday night asking for details about who the outside counsel might be.

"This is not a criminal trial for which the involvement of an experienced sex crimes prosecutor would be appropriate," Michael Bromwich, an attorney for Ford, wrote in a letter to the committee. "The goal should be to develop the relevant facts, not try a case."

Meanwhile, committee lawyers have reached out to lawyers for Debra Ramirez, who detailed separate allegations of inappropriate sexual behavior against Kavanaugh to The New Yorker, and asked whether she has any evidence, in addition to what was printed in the magazine, to support her accusations, and whether she would provide the evidence to the committee.

Ramirez's attorney John Clune tweeted "Our client stands by the facts of the New Yorker story as reported." He also said, "We are in contact with the Senate Judiciary Committee to determine the best process to provide Senators with additional information. We remain adamant that an FBI investigation, where all witnesses are questioned under threat of perjury, is the only way to get the truth. Our client remains willing to cooperate with such an inquiry."

At least one Senate Republican appeared open to the idea of such an investigation. CNN asked Alaska GOP Sen. Lisa Murkowski, a key swing vote, if there should be a full FBI probe into the allegations.

She responded, "It would sure clear up all the questions, wouldn't it?"