The Supreme Court cleared the way yesterday for enforcement of a clean-air plan for New York City that officials there say will jeopardize the city's existence as a commercial center.

The purpose of the plan is to curb automotive air pollution by reducing the use of motor vehicles for travel in and to Manhattan.

The court denied pleas by Mayor Abraham Beame and Gov. Hugh Carey for review of a ruling that upheld the plan.

One of the city's complaints was that the plan was the product of an "unauthorized pact" devised by former Mayor John Lindsay and former Gov. Nelson Rockfeller in the comforting knowledge that it wouldn't take effect until after they left office.

The federal Environmental Protection Agency approved tha plan in June, 1973. Major features include tolls on all 11 free bridges across the Harlem and East rivers, restrictions on taxi cruising, elimination of both on-street and off-street parking in certain sectors and of on-street parking in the midtown core, and a ban on freight deliveries during business hours.

The predicted result - a 50 per cent reduction in vehicle entry into Manhattan by 1980 - would be "disastrous," the city told the Supreme Court.

The bridges are "literally and figuratively the arteries of the city's commerce," it was argued. Moreover, tolls would cause "massive traffic snarls and potential loss of valuable real estate" to toll station plazas.

Seventeen months after EPA approved the plan, Friends of the Earth and other environmental groups sued for a federal court order to compel compliance.

Counsel for the state acknowledged that the plan was "legally enforceable" and "legally adequate" - and also that officials apparently had no intention to implement certain parts of it. "If there is a legal ground for such a refusal, we have not been able to find it," he told the court.

After the court initially rebuffed the environmental groups, and after more litigating, the Second U.S. Circuit Court of Appeals ruled for them last January.

"The picture before us is one where the city, having voluntarily cooperated with the state in the drafting and promulgation of the very strategies now attacked by it, seeks in effect to renege on its own creation and commitment," the Second Circuit said.

"The architects of the plan were not Congress or the EPA but the State and City of New York . . . In clear and unmistakable terms the plan obligates them to carry out the very strategies which the city now contends that it cannot be order to enforce." POLICE INTERROGATION

Three years ago, Rufus J. Mincey lay helpless in the intensive care unit of a Tucson hospital. A tube carried oxygen through his throat, a second tube went through his penis to his bladder, and a third tube through his nose to his stomach. Other tubes carried fluids into his veins. He was in a near coma from a gunshot wound, and in pain he later termed almost unbearable.

For an hour, Mincey, then 23, was questioned by a detective who had obtained permission by telling a nurse that Mincey had been charged with the murder of a plainclothesman who had made a narcotics raid on Mincey's apartment.

When he was conscious, Mincey wrote down six pages of answers to the detective's questions. Two of the answers were used later to impeach his testimony at the trial that led to his conviction for felony murder, among other offenses. He is now in prison.

The Supreme Court took other actions:

Yesterday, the justices agreed to review a decision by the Arizona Supreme Court that the interrogation did not deny Mincey's constitutional rights to protection against self-incrimination and to due process and counsel. NUDE DANCERS

Several years ago, California's Alcoholic Beverage Control (ABC) Board adopted regulations intended to curb oral copulation between entertainers and customers and other sexual acts in bars featuring nude dancing.

In 1972, the Supreme Court upheld the regulations in a 6-to-3 decision based on the 21st Amendment to the federal Constitution, which, in repealing Prohibition, banned importation of liquor into a state in violation of its laws. One dissenter protested that nothing in the amendment's language or history authorizes a state to use its liquor-licensing power "for the deliberate inhibition of protected, even if distasteful, forms of expression."

Then, in San Diego, Paul A. Richter instituted nude dancing in a bar-theater with fixed seats and separation of entertainers from patrons. The ABC revoked his liquor license.

In an appeals hearing, dance drama expert Virginia F. Chase testified that the dancing at Richter's place, The Body Shop, was very much the same as that of "modern dance troupes and ballets"; that modern ballet companies sometimes perform in the nude, and that one has done so on public television in New York City. She said she personally found dances at The Body Shop "less sensual."

Yesterday, the court let stand a lower-court decision upholding the revocation of Richter's license.