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Judge Kimba M. Wood withdrew today from consideration for Attorney General after the White House learned she had employed an illegal immigrant as a baby sitter before it became illegal to do so.

That stunning setback left President Clinton scrambling for the third time to fill the post.

There was no evidence that Judge Wood, who sits on the Federal District Court in New York, did anything illegal, but White House officials said they told her to withdraw because they feared the kind of public outcry that struck down the Administration’s first choice for Attorney General, Zoe Baird, who had employed two illegal aliens for household work. A Blank List

White House officials said they were angry at Judge Wood because she had not told Mr. Clinton and other officials about her baby sitter, even when she had been directly asked. In her statement, however, Judge Wood said she had not misled the White House.

After the hasty search for a first nominee, then the rush to replace Ms. Baird, the Clinton Administration was forced by Judge Wood’s withdrawal to start virtually from the beginning in looking for the nation’s top law-enforcement official.

“They have nobody on their list now, period,” said a Democratic Senator who is close to the White House. “They’ve got to start from scratch.”

As late as Thursday evening, White House officials confidently said Mr. Clinton planned to announce Judge Wood’s selection as soon as background checks were completed. But what the officials viewed as a done deal disintegrated later that night as officials questioned Judge Wood and studied documents she had submitted. Trained to Be Playboy Bunny

The sudden turnabout on Judge Wood is a blow to Mr. Clinton, who two weeks ago withdrew Ms. Baird’s name after she admitted she had hired the illegal immigrants and had knowingly neglected to pay the required taxes for household employees.

Tonight the White House issued a statement on behalf of Mr. Clinton. “I understand and respect Judge Wood’s decision not to proceed further with the possibility of being nominated as Attorney General,” it said. “I was greatly impressed with her as a lawyer, a judge and a person. I respect her legal talents, judicial record and integrity. I wish her well.”

The White House officials said they had also recently discovered that Judge Wood had briefly trained as a Playboy bunny years ago when she was a student in London and that they feared that that might become the source of jokes.

In the statement issued by her lawyer’s office in New York, Judge Wood did not cite her stint as a Playboy trainee but said the issue was her hiring of an illegal immigrant from Trinidad, who worked for her for seven years. Judge Wood said she did not act illegally because her baby sitter was hired in March 1986, several months before the enactment of a Federal law making hiring of illegal aliens unlawful. The baby sitter obtained legal residency in December 1987, she said.

“On Jan. 29, I met with the President at the White House to discuss the possibility of my appointment,” she wrote. “In the course of a wide-ranging discussion of policy issues, I was asked if I had a ‘Zoe Baird’ problem. I said I did not. And I do not.”

Judge Wood went on to say: “I have fulfilled every legal requirement with respect to the employment of our babysitter. Nevertheless, and after further consultations, I have concluded that in the current political environment, proceeding further with the possibility of my nomination would be inappropriate.” Problems With Backups

Complicating the matter is that the President is not ready to name a substitute candidate. Officials had initially said that if Judge Wood did not pass the background checks they would probably turn to Charles F. C. Ruff, a Washington lawyer and former senior Justice Department official, or former Gov. Gerald L. Baliles of Virginia. But today, they said that questions had been raised about whether Mr. Ruff had employed an illegal alien and that the President was not ready to pick Mr. Baliles.

George Stephanopoulos, the White House communications director, sought in an interview tonight to play down any implication that the Administration was at fault. He said Judge Wood was asked about the issue of illegal aliens once by the President and twice by Bernard W. Nussbaum, the White House chief counsel.

“The White House search process discovered the problem,” Mr. Stephanopoulos said. “Judge Wood was asked about this matter twice before she interviewed with the President and once in her interview with the President. As the process moved forward, the White House did discover it because she delivered financial records that she had hired a baby sitter who was in the country illegally. After this information was discovered, and after consultation with the White House, Judge Wood decided to withdraw.” 

Asked about the disclosure that she had trained to be a Playboy bunny, Mr. Stephanopoulos said, “I just don’t know anything about it.”

Officials close to the White House said the trouble developed in part because President Clinton, pressed by his wife, Hillary Rodham Clinton, insisted on finding a woman for Attorney General, which limited the field of Democratic contenders with a law-enforcement background. The problem with Judge Wood, they said, was that although she is a respected jurist, she lacked the law-enforcement and managerial credentials for the post. So when the disclosures arose, there was no great desire by Senator Joseph R. Biden Jr., the Delaware Democrat who is chairman of the Judiciary Commitee, or other influential players to press her case. A Lark in London

Judge Wood is 49 years old and was appointed to the court by President Ronald Reagan in 1988. She had no experience with criminal cases before her appointment and had never conducted a trial before a jury. But she has earned the respect of other judges and lawyers who have come before her, and the President and Mrs. Clinton are said to have been favorably impressed when each interviewed her last week.

People close to the situation said Mr. Nussbaum contacted Judge Wood on Thursday to tell her that he had heard a rumor that she had put herself through the London School of Economics as a Playboy bunny.

According to people familiar with the conversation, Judge Wood told Mr. Nussbaum that in 1966 she was a student in London and that on a lark she had signed up for the bunny trainee program for the Playboy Club there. She told him she quit after five days, before actually being employed by the club or drawing a paycheck.

Mr. Nussbaum is said to have told Judge Wood that the episode would not disqualify her.

Even after the disclosures were made, officials said, Judge Wood wanted the White House to press ahead, as did some Administration officials. But the White House backed down, they said, after learning that Mr. Biden and others had serious reservations about the nomination.

As early as Thursday night, the White House struggled to contain the political fallout. Hours after some Administration officials told reporters an announcement on Judge Wood would be forthcoming as long as background checks did not turn up anything serious, officials called reporters at home after midnight to urge them to back off the story. At the time, they did not say there were developments that had diminished Judge Wood’s prospects. ‘They Want Squeaky Clean’

By this morning, White House officials said Judge Wood’s selection was in grave doubt, and as the day wore on and rumors flew through the capital it looked increasingly likely that her candidacy might not last the day.

Administration officials said Judge Wood and her husband, Michael Kramer, a political columnist for Time magazine, spent much of the day closeted with Administration officials in the hope of salvaging the nomination.

Officials involved in the background checks said the White House was being far more cautious than in the checks of Ms. Baird. They said officials were not only concerned about finding instances of illegality but anything that could raise any appearance of impropriety. “They want squeaky clean,” said one official involved in the process. “They’re worried about how all this will play in Peoria.”

Another official who was deeply involved in examining Judge Wood’s background expressed sympathy for the judge and said: “Under any other circumstances, this would have been totally ignored. But we can’t afford the battle right now. It’s a perception problem.”

Fellow judges who serve with Judge Wood in the Federal Courthouse in lower Manhattan also expressed sympathy for her.

“I’m very, deeply disappointed for her sake,” said Judge Thomas P. Griesa. “I think she would have made an outstanding Attorney General. “I’m really disappointed.”