IF YOU WATCH Hill Street Blues, or any television crime show, you know that the first thing the cops do after they arrest the robber is read him his "rights." That is the result of the Supreme Court's decision in the case of Ernest Miranda v. Arizona, the case around which this book revolves. When the Miranda case started, 20 years ago last March, there was little to distinguish it from any year's crop of kidnaping and rape cases. But by the time it was over, Miranda had become a word that tormented policemen, outraged politicans, and haunted the Supreme Court.

For it was in the Miranda case that the Court said police are required by the Constitution to tell all those arrested of their legal rights. Any confession made to the police by a person who had not been told of his rights, the Court decreed, could not be used in evidence against him.

As soon as word of the decision reached them, law enforcement officers all over the country told the public it meant they would lose the war on crime. Prisoners who were told their rights (and allowed to exercise them) would not confess, the police argued, and without confessions many criminals would be turned loose to rape and rob again.

A year after Miranda's original conviction, another Arizonan, Sen. Barry Goldwater, introduced the phrase "violence in our streets" into the American political dialogue. The phrase, with all the baggage it quickly came to carry, became the centerpiece of his ill-fated presidential campaign. The Supreme Court, he and many others contended, was coddling criminals and giving them too many rights. That was the real cause, they said, of the rising crime rate; the streets would become safe again if only the Court's reading of the Bill of Rights could be changed.

The Supreme Court's Miranda decision two years later, and the immediate police denunciation of it, gave those who agreed the rallying point they needed. Richard Nixon campaigned hard against the Court in 1968 and promised to nominate only justices who would reverse a judicial philosophy he regarded as "too soft on crime."

Washington writer Liva Baker has used Miranda and the uproar around it as the basis for a brilliant contemporary history of the Supreme Court. The book brings back, and puts into focus, a host of memories from an era that yielded center stage to the Vietnam war in the early 1970s as quickly as it had replaced the anti-communism show more than a decade earlier. The philosophical struggle between Warren Burger and David Bazelon on the United States Court of Appeals here is part of this story, for that was what stamped Burger as the kind of judge Nixon wanted to carry out his campaign promises. So are the political battles between President Johnson and Congress, first over how to attack crime and later over his nomination of Abe Fortas to be chief justice--the job that went to Burger after the 1968 election. Wrapped around such matters are vignettes of the justices, scenes from jailhouses and courtrooms, and judgments by the author on why things turned out the way they did.

The book's enormous wealth of detail makes it easy to believe the publisher's statement that Baker devoted six years to research. We learn the fate of Ernest Miranda, of course: He was convicted again without use of the confession which was the heart of the whole controversy, served seven years in prison, and eventually died in a bar fight in Phoenix, (a victim of the street crime the Court decision which bears his name was said to encourage). But before he was murdered, his futile ex-con pleas for rehabilitation ironically echoed the speeches being made about the desperate need for prison reform by the most important anti-Miranda figure still prominent in public affairs, Chief Justice Burger.

It is the interplay of events like these that make Baker's book a lively and thought-provoking exploration of the relationships between law, politics, public opinion, and crime. Perhaps everyone who has participated, directly or marginally, in the long argument about the Miranda decision (or the way the Supreme Court squares the commands of the Bill of Rights and the needs of law enforcement officers) will find something in her book to criticize. I think, for instance, that in trying to figure out why judges vote the way they do in criminal law cases, she gives too much weight to the environment in which the judges lived and worked before becoming judges. But the vast research she has put into this book entitles her to such an opinion.

Baker's ultimate conclusion may come as a surprise. Despite attacks on the Miranda decision by a president, the Congress, a chief justice, other justices, and most of the law enforcement community, it survives. True, Miranda is now but a shadow of what it seemed it might become on the day Chief Justice Earl Warren read the opinion from the bench. It has been narrowed, weakened, and undercut. But, while the Burger Court has fulfilled many of President Nixon's dreams, the chief justice has never been able to muster the votes necessary to flatly overrule Miranda. Its continued vitality, of course, is still threatened (by efforts that will resume next fall to eliminate the exclusionary rule on which its effectiveness rests).

Baker's research, however, shows that several state supreme courts have refused to go along with that weakening process and are establishing as a matter of state law, beyond the reach of the Supreme Court, the principles on which Miranda was based. It would be one of the supreme ironies in judicial history if the state courts stepped in to become the protectors of the rights of defendants, counteracting the huge effort that has goneeinto undoing Miranda and the rest of the Warren Court's revolution in the criminal law. Baker sees that coming.