The Supreme Court yesterday agreed to review the most serious legal challenge yet to the Reagan administration's deregulation efforts: an appeals court ruling reinstating air bag and automatic seat belt requirements revoked by the administration.

The case, which will be decided by next summer, could determine whether all new cars will some day include such "passive restraints."

It also tests the power of the courts generally to ride herd on regulatory agencies and could thus affect all of the administration's attempts to reverse the course of federal regulation. It could also help determine the future availability of the judiciary as a forum for challenging regulatory decisions.

The dispute continues a decade-long skirmish over the discretion of regulatory agencies between liberal appointees on the U.S. Court of Appeals for the District of Columbia and conservatives on the U.S. Supreme Court.

Abner Mikva, the liberal former congressman from Illinois and a Carter appointee to the appeals court, wrote the June, 1982, ruling that shot down the administration's effort to free the automobile industry of the costly safety standard.

The standard would have required that large and mid-size cars built after Sept. 1, 1982, and all cars built after Sept. 1, 1983, include "passive restraints" -- that is, air bags or automatic seat belts. Its supporters say it could prevent 9,000 deaths, 65,000 injuries and save $2.4 billion per year.

The administration had placed the standard near the top of its regulatory "hit list," however, and in October, 1981, the National Highway Traffic Safety Administration withdrew the regulation, overruling its own staff.

The agency, using the kind of cost-benefit analysis required under a Reagan executive order, said the standard would cost "in excess of $1 billion" without the certainty that it would "achieve significant safety benefits."

Responding to suits brought by the insurance industry, among others, a three-judge panel of the appeals court ruled that the rescission was "a paradigm of arbitrary and capricious agency action . . . unsupported by evidence" or by "reasoned decision-making."

The car manufacturers and the government appealed to the Supreme Court (Motor Vehicle Manufacturers Association vs. State Farm Insurance Co., et al.). The ruling, the government argued, "may substantially impede the ability of other federal agencies to revise their existing policies and chill the agencies in their development of new policies for fear of judicial obstacles to subsequent modification."

In other action yesterday:

* The court again agreed to consider the authority of federal courts to intervene in sentencing decisions made by lower courts. The case, Solem vs. Helm, stems from the life sentence without parole imposed under South Dakota's chronic offender statute on Jerry Buckley Helm after seven separate convictions for crimes ranging from drunken driving to check bouncing.

The 8th U.S. Circuit Court of Appeals, citing the Constitution's prohibition on cruel and unusual punishment, reversed the sentence as disproportionate to the crimes. In two major cases recently, including a Virginia dispute over a 40-year sentence for possession of marijuana, the justices have warned lower federal courts not to tamper with sentencing decisions.

* The justices said they would consider how much access outsiders may have under the Freedom of Information Act to documents generated by government lawyers preparing for court cases. The case, FTC vs. Grolier, stems from a Federal Trade Commission investigation of the Americana Corp., a subsidiary of Grolier Inc., and a subsequent attempt by Grolier to see material relating to the probe.

The Court of Appeals for the District of Columbia said that once litigation is terminated, such documents may no longer be exempted under the FOIA.

The government appealed, saying the ruling "will have a serious adverse impact upon the government's ability to conduct civil and criminal litigation effectively."

* The justices upheld a decision denying labor unions the same political fund-raising freedom enjoyed by corporations under federal election law.

The appeal was brought by the International Association of Machinists, protesting a lower court ruling under which corporate political action committees may solicit funds from their employes but labor PACs must wait for voluntary contributions from their members.

The machinists' union contended that the corporate solicitations subjected employes to "coercive" fund-raising methods that violated their right of free speech. A unanimous Court of Appeals for the District of Columbia turned down the machinists' challenge as did the Supreme Court yesterday in affirming the ruling without comment (International Association of Machinists vs. Federal Election Commission, et al.).

* The court said it would review the death sentence imposed on Elwood Barclay for the random slaying of a white teen-ager in Jacksonville, Fla., as part of an alleged plan by a self-styled black revolutionary to avenge the treatment of blacks by whites.

The issue in the case (Barclay vs. Florida) is the jury's latitude to weigh aggravating circumstances when considering the death sentence.

The court said it would consider the authority of police to search a purse when booking someone in a police station. The dispute, Illinois vs. LaFayette, originated when police in Kankakee, Ill., searched a man's purse while booking him for disorderly conduct and discovered drugs that were alleged to be amphetamines.

The Illinois Appellate Court ruled that the evidence was inadmissible, saying the police invaded the man's privacy without sufficient need.

* The court, without comment, declined to review a decision (Stover vs. Rau, etc.,) requiring separate, rather than combined, lawsuits stemming from the collapse of a "skywalk" at the Kansas City Hyatt Regency Hotel in 1981.

The disaster killed 114 people and injured many others. It also produced at least 150 suits in state and federal courts seeking to collect damages from the hotel and those who helped build it.

Fearing that there might not be enough money to go around, some lawyers and a lower court judge in Kansas City preferred a class action, a combined suit for everyone, followed by apportioned distribution of money if successful.

Other lawyers and the 8th U.S. Circuit Court of Appeals favored separate handling of the suits. Among them were the lawyers for the hotel, which has already settled out of court with many plaintiffs.