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."