A federal judge, in the first decision of its kind, ruled yesterday that city officials in Yonkers, N.Y., maintained a segregated school system by refusing to build low-income housing on the exclusive east side of town for more than three decades.

In a 600-page decision, U.S. District Court Judge Leonard B. Sand detailed the causal relationship between segregated neighborhoods and segregated schools.

He said that Yonkers officials are liable for the perpetuation of mostly white and mostly black schools because they deliberately relegated all subsidized housing projects to the minority neighborhoods on the city's west side.

Civil rights lawyers said the ruling would provide a potent legal weapon for private plaintiffs to challenge patterns of housing and school segregation in other cities, but that they do not expect the Reagan administration to bring such cases.

The Justice Department, which sued Yonkers in the final days of the Carter administration, briefly considered dropping the case after President Reagan took office, but pressed ahead with the NAACP as a joint plaintiff.

Sand scheduled hearings for next month to consider what remedies should be imposed on the New York City suburb of 200,000.

"The unusual thing about this case is we alleged that the city's housing discrimination was a cause of school segregation, and the judge agreed with us," said Justice Department attorney Sarah Vanderwicken.

The city had contended that segregation was the product of people moving where they wanted.

Michael Sussman, an attorney for the NAACP, said the Reagan administration has brought no similar cases and that it is up to civil rights groups to attack official segregation elsewhere.

"The kind of objective evidence presented in Yonkers can be found in many other places," Sussman said. "The pattern of state-supported segregation of housing is one that's replicated everywhere, and the obvious consequence of that is school segregation. Until we acknowledge that, we'll have the continued perpetuation of an underclass."

John Zakian, a spokesman for Yonkers Mayor Angelo Martinelli, said the ruling was "no surprise" and that the city hopes to settle the case in the coming weeks. He said Martinelli was reelected this month after arguing that "we are going to have to put low-income housing in east Yonkers," but that the may- or's attempts to settle the suit have been blocked by the city council.

Arthur J. Doran, the city council's attorney, said it would be difficult for the financially strapped city to pursue an appeal. "Having spent $8 million to prove you were correct, and finding out the court disagrees with you, is a disappointment," he said.

The Westchester County community is split down the middle by the Saw Mill River Parkway, which has served as a racial dividing line. Expensive split-level homes and 90 percent white schools cover the hills to the east, while the rundown west side features minority schools and more than 30 public housing projects.

After hearing more than 100 witnesses, the judge ruled that city officials deliberately concentrated the subsidized housing on the west side, a fact that led to a cutoff of federal community development funds two years ago.

Sand cited the testimony of former Yonkers mayor and former lieutenant governor Alfred del Bello which said that race had been a factor in housing decisions.

Sand also ruled that city and school officials had redrawn school boundaries, closed schools, reassigned teachers on the basis of race and steered minority students into certain programs in a deliberate effort to maintain segregation in schools.

Despite extensive settlement negotiations, the city council refused to approve two sites on the affluent east side for low-income housing, and the school board rejected two modest busing plans.

Emotions have run high on both sides. Herman Keith, former president of the Yonkers NAACP, told of being unable to buy a house on the east side and watching his children reassigned to minority schools.

But Michael Cipriani, a former council member and an opponent of subsidized housing, said in a 1983 interview: "My home is worth $225,000. I don't want any apartment building next to me. That's what I moved to the suburbs for."