A divided Supreme Court yesterday left intact a racial desegregation plan for Cleveland public schools that may necessitate crosstown busing of 52,000 students.

By 6 to 3, the justices rejected a challenge by the Cleveland Board of Education to the court-ordered plan, part of which went into effect last September.

Chief Justice Warren E. Burger and Justices William H. Rehnquist and Lewis F. Powell Jr. voted to hear the school board's appeal of the plan, which requires every school in the 91,000-student district to reflect approximately the racial makeup of the district. About two-thirds of Cleveland's public school students are black.

The three dissenters said that "even if the Constitution required it, and it were possible for federal courts to do it, no equitable decree can fashion an 'Emerald City' where all races, ethnic groups and persons of various income levels live side-by-side in a large metropolitan area."

In other actions yesterday the court:

Gave the federal government permission to enforce a stringent strip mining law in Virginia until it can formally appeal a decision striking down part of the law.

U.S. District Court Judge Glen Williams in Abingdon, Va., had struck down important provisions of the law, which was designed as a tough check on evironmental problems caused by strip-mining coal. The justices yesterday stayed enforcement of Williams ruling.

Let stand a ruling allowing dismissal of a Los Angeles worker who, on religious grounds, refused to join a union in a plant where union membership was required.

Kenneth Yott, a Rockwell International worker, was fired after he rejected several alternatives to union membership offered as a way of accommodating his beliefs.

Two lower courts found that Yott, a member of a religious organization called the Church That Is Christ's Body, held sincere beliefs but that the union and company had made a "good-faith effort" to accommodate them, as is required by prior court rulings.

Agreed to consider whether states may alter the method of calculating a prisoner's parole after imprisonment.

The case was brought by a Florida inmate, Hoyt Weaver, who claimed that more then two years was added to his term by a state law passed after he went to prison.

The Florida attorney general argued that inmates have no legal "right to parole," and that the terms of parole can be "withdrawn, modified or denied" at any time.

Let stand a decision that a dress code -- imposed only on women employes by a Chicago savings institution -- was discriminatory. The Talman Federal Savings and Loan Association required female employes to wear uniforms but required only that male counterparts dress "appropriately."

Lower courts held this was illegal sex discrimination.

Agreed to decide whether murder defendants must receive Miranda-type warnings before psychiatric testing if the results are used to determine the court's punishment.

Ernest Benjamin Smith was convicted and sentenced to death for the murder of a Dallas grocery store clerk during a 1973 robbery. While Smith was awaiting trial, a state judge ordered a psychiatrist examination, with which Smith cooperated.

The psychiatrist then testified at the defendant's sentencing hearing, saying he was a "severe sociopath [who would] continue his previous behavior."

Lower courts held that evidence based on such an examination may not be used unless the defendant was warned he had a right to remain silent and could end the exam whenever he wished.