The Supreme Court yesterday deadlocked on the crucial issue of whether presidents and their advisers can be sued for monetary damages when they violate the law.

The court, with Justice William Rehnquist not voting, split 4 to 4 over a damage suit brought by former National Society Council staff aide Morton Halperin against former president Nixon, his attorney general, John N. Mitchell, and his chief of staff, H.r. Haldeman, after Halperin discovered that the Nixon White House had illegally tapped his phones. Rehnquist worked for Mitchell at the time of the taps.

The tie vote automatically affirms the victory Halperin won in the lower court, so he and his family may be able to collect money from Nixon and his former advisers. The issue of the amount, and whether former national security affairs adviser Henry A. Kissinger must also pay, is up to the lower courts.

But tie votes have to impact on other cases and the government's argument, that presidents and their aides should have immunity from such suits, remains unresolved. The government contended that allowing the suits, as the Court of Appeals for the District of Columbia did in the Halperin case, would seriously threaten presidential power.

The justices may answer the question next year. At the same time that they split on the Halperin case yesterday, they agreed to review a damage suit against Nixon brought by former Pentagon "whistle-blower" A. Ernest Fitzgerald over his dismissal by the Nixon administration.

Mark Lynch, Halperin's American Civil Liberties Union lawyer, said yesterday he believed Halperin would cllect his money. But the Supreme Court could hold up any award, and possibly even deny it, depending on when and how the justices resolve the Fitzgerald case next year.

In other action yesterday:

The court gave governments a constitutional way to restrict the roving solicitations and pamphleteering of Krishna society adherents, ruling that they can be confined to a booth in some public places.

Justic Byron White said that the First Amendment allows such a restriction so long as there is a good reason for it and it is applied equally to all other groups soliciting or proselytizing.

The justices reversed the Minnesota Supreme Court, which said a Minnesota State Fair restriction breached constitutional safeguards for religious practices. And they rejected the arguments of ACLU and four justices that the state fair rule was an overbroad and unnecessary infringement of the right to distribute literature.

The ruling in Heffron v. Internation Society for Krishna Consciousness was one in a line of cases concerning how far government can go to restrict otherwise protected rights of free expression. Bans or restrictions on specific points of view are impermissible, the court has held. But necessary and narrow restrictions on the "time, place and manner" of expression may be legimate.

The Minnesota State Fair rule, White said, is valid because it left the Krishnas with an alternative, the booth. The booths were allocated on a first-come, first-served basis, he said, meaning that there was no discrimination in implemeting the restriction.

Minnesota's reason for the restriction, to maintain the orderly movement of crowds, was also acceptable, White wrote for the majority.

Justices William J. Brennan, Thurgood Marshall, John Paul Stevens together, and Justice Harry A. Blackmun separately, wrote partial dissents. tThey said the restrictions were constitutional limitations on fund raising and the selling of literature. But they, and the ACLU, said it was an unreasonable limitation on the distribution of literature.

In an unsigned opinion, the court allowed the state of New York to ban topless dancing in bars.

The ruling in New York State Liquor Authority v. Bellanca follows a controversial decision two weeks ago striking down a Mount Ephraim, N.J., zoning ordiance used to ban nude dancing in any establishment, bar or otherwise. The difference, the court said yesterday, was that states have almost total power to regulate the sale of liquor under the constitutional amendment repealing prohibition.

"Although some may quarrel with the wisdom" of the legislation banning topless dancing on premises where alcohol is served, the court said, "and may consider topless dancing a harmless diversion, the 21st Amendment makes that a policy judgment for the state legislature, not the court."

The decision, issued summarily without full arguments, reversed a New York Court of Appeals judgment. Justice Brennan dissented saying the case should be full considered by the Supreme Court.

Justice Stevens also disagreed. The ruling allows states to ban any activity in bars, however much protection it finds in the Constitution, he said. He called that a "blatantly incorrect" reading of the 21st Amendment.

In a 6-to-3 ruling, the court made one of its few exceptions to the requirement that police have probable cause and a warrant to detain someone. The justices ruled that police could detain the occupant of a house named in a search warrant while they are conducting the search.

The ruling in Michigan v. Summers stems from a Detroit narcotics raid. Police had a warrant to search the home of George Summers. But they did not have a warrant to detain or arrest Summers. When they arrived at Summers' house, he was on his way out. Police detained him until their search, which produced narcotics, was completed and then charged with possession of heroin.

In the past, the court has allowed detentions without a warrant to search for weapons that could be used to harm police. And it has allowed warrantless detentions by border police for illegal aliens.

Yesterday the court added a new situation: A warrant to search a home, Stevens wrote, "implicity carries with it the limited authority to detain the occupants of the premises while a proper search is conducted."

Justic Potter Stewart, joined by Brennan and Marshall, read a strongly worded dissent from the bench yesterday. The majority ruling ignores "the protections that the Fourth Amendment guarantees to us all," Stewart said.

The Halperin case in which the court deadlocked yesterday was one of the few remaining Watergate-era controversies still in the courts. The White House ordered wiretaps on the personal phones of Halperin and others in 1969 in an effort to track down the source of news leaks, including one that exposed secret B52 raids in Cambodia during the Vietnam war.

Halperin filed suit, charging both constitutional violations of his right to privacy and violations of the federal wiretap law, after the taps were exposed during the 1973 "Pentagon Papers" trial of Daniel Ellsberg. (Kissinger, Halperin's boss at the National Security Council, was also sued. But the lower court decisions left room for further proceedings about his liability.)

In 1977, the Supreme Court ruled in an unrelated case (Butz v. Economou ) that officials from Cabinet level on down were liable to damage suits. But the justices had never addressed the liability of the White House.

In the Halperin case, the U.S. Court of Appeals for the District of Columbia decided against absolute immunity. Liability is "mandated by our tradition of equal justice under law," wrote then Chief Judge J. Skelly Wright. "The president is the elected chief executive of our government, not an omniscient leder cloaked in mystical powers."

The government appealed to the Supreme Court, arguing that the denial of immunity would dangerously threaten the president's ability to function by confronting him with constant lawsuits and would breach the separation of powers between the executive and judicial branches of government.

Because of the tie vote yesterday, the question remains for consideration in the Fitzgerald case. The full court should be able to vote in that case, since Rehnquist played no known role in the Fitzgerald controversy. Because yesterday's action was by an equally divided court, the vote of each justice was not revealed. Thus it is not clear how the replacement of Justice Stewart, who will retire July 3, might influence the outcome.