Kathryn Watson and Emily Tillett, CBS News

WASHINGTON (CBS News) – The woman who has accused Supreme Court Justice nominee Brett Kavanaugh of sexual misconduct, Christine Blasey Ford, is calling for an FBI investigation before testifying in front of the Senate Judiciary Committee. And Ford’s lawyers admonished the committee for scheduling the hearing so soon after her allegations became public.

“While Dr. Ford’s life was being turned upside down, you and your staff scheduled a public hearing for her to testify at the same table as Judge Kavanaugh in front of two dozen U.S. senators on national television to relive this traumatic and harrowing incident,” said a letter Tuesday evening from Ford’s lawyers to Sen. Charles Grassley, the committee chairman.

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The committee invited both Kavanaugh and Ford to testify on the allegations, and Kavanaugh accepted. Mark Judge, who allegedly was also at the party in question in the 1980s, and in the room with Kavanaugh, said through his attorney he has no memory of the alleged incident and does not wish to testify publicly.

Democrats are accusing Grassley of trying to rush through the confirmation. They say that two witnesses are insufficient, and the rushed nature could lead to the “mistakes” of the Anita Hill hearings during Clarence Thomas’ Supreme Court confirmation hearings.

The hearing scheduled for Monday represents a significant change in Kavanaugh’s confirmation process. The committee had planned a meeting Thursday, but had planned it for next Tuesday, after Kavanaugh and Ford had a chance to testify.

Even if Ford does not appear on Monday, Republicans could continue to give Kavanaugh the opportunity address the allegations.

The letter on Tuesday said that Ford “wants to cooperate with the Committee and with law enforcement.” The lawyers said an FBI investigation should come first. “A full investigation by law enforcement officials will ensure that the crucial facts and witnesses in this matter are assessed in a non-partisan manner, and that the Committee is fully informed before conducting any hearing or making any decisions.”

The lawyers said that Ford has been the target of “vicious harassment and even death threats” and that her family has relocated.

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Read Ford’s letter to the Senate Judiciary Committee here.

Context on the FBI’s role in investigating Kavanaugh

Democrats — and now Ford — are urging the FBI to reopen the investigation into Kavanaugh’s history, which was essentially a background check. According to CBS News contributor Ron Hosko, who is a former assistant director of the FBI, the FBI could investigate if evidence arose of a federal crime or of a national security matter while investigators were conducting Kavanaugh’s background check. (For instance, if a federal crime had been committed 35 years ago and beyond the statute of limitations, the bureau might opt not to investigate).

The FBI’s investigative work here is neither criminal nor national security.  It is, Hosko explains, a background investigation led by the Security Division for a customer — the White House. The results are packaged and provided to the customer.

There is no local criminal investigation in this case, and the allegations so far do not fall under federal criminal statutes or national security areas. The FBI therefore puts the information in Kavanaugh’s background check folder, which the FBI has already said it did. The White House must then decide if the FBI should investigate the matter further.

A U.S. official tells CBS News that under the existing memorandum of understanding, the White House would need to ask the FBI to look into the allegations raised by Ford.

Based on such a request from the White House, the bureau would then move forward.

— Kathryn Watson, Emily Tillett, Grace Segers; Andres Triay contributed to this report.

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