"Out of respect for the integrity of the process, we will have no further comment at this time," Ramirez's lawyer, John Clune, said in a statement.
Ramirez, a former Yale University classmate of Kavanaugh's, said the judge exposed himself to her at a 1983 party while she and friends were playing a drinking game.
Kavanaugh denied the accusation.
"This alleged event from 35 years ago did not happen," he said in a statement. "The people who knew me then know that this did not happen and have said so. This is a smear, plain and simple."
Ramirez contacted several former classmates to ask if they recalled the incident and said she couldn't be sure it was Kavanaugh.
On Friday, President Donald Trump ordered an FBI investigation into Kavanaugh after Sens. Jeff Flake, R-Ariz., and Lisa Murkowski, R-Alaska, said they wouldn't vote in favor of the judge's confirmation without one.
Flake suggested the probe be limited to Ford's allegations against Kavanaugh.
On Thursday, Ford tearfully reiterated her account of the night she said Kavanaugh attacked her at a party they and at least four others attended at a house near Bethesda, Md.
Ford told the Senate judiciary committee that Kavanaugh and his friend Mark Judge "were visibly drunk" and attacked her in one of the bedrooms at the house. She said Kavanaugh and Judge were "extremely inebriated ... and the other people at the party were not."
"I was pushed onto the bed and Brett got on top of me," she told the panel, adding she believed he was going to rape her.
"I tried to yell for help. When I did, Brett put his hand over my mouth to stop me from screaming. It was hard for me to breathe, and I thought that Brett was accidentally going to kill me."
She said she's never forgotten Kavanaugh and Judge's "uproarious laughter ... and their having fun at my expense."
Ford said Judge jumped onto the bed, knocking her and Kavanaugh over, at which point she ran from the room and locked herself in a bathroom across the hall. After hearing Kavanaugh and Judge go back downstairs, Ford said she left the house.
Testifying after Ford, Kavanaugh denied ever attacking her in an emotional rebuttal.
"I never did anything remotely resembling what Dr. Ford describes," he said.
Trump has repeatedly offered support for Kavanaugh, his second nominee to the Supreme Court. On Saturday, the president told reporters he thinks the FBI probe is going "very well."
"I don't think there's ever been any person who's been under scrutiny like he has. I think it's been a very tough process. He's a good man. He's a great judge," Trump said.
He said Flake's request for an investigation was a "blessing in disguise."
"I think frankly the FBI has a chance to reveal a lot of different things. I'd like to find out who leaked the papers," he said, referring to a confidential letter Ford wrote to Sen. Dianne Feinstein, D-Calif., detailing the allegations.
"Was it Sen. Feinstein? Certainly her body language was not exactly very good when they asked her that question. I would like to find out as part of it who leaked the papers. Which Democrat leaked the papers."