Acting in a Maryland case with wide implications for personal privacy, the Supreme Court agreed yesterday to decide whether a device that monitors and records the numbers dialed on a telephone can be installed without a search warrant or court order.

The state's highest tribunal ruled 4 to 3 last July that Baltimore police did not violate the Constitution when they had the phone company install the device, called a pen register, in its own offices to record the numbers dialed by Michael Lee Smith at his home.

The pen register provided evidence that led to Smith's conviction for the 1976 street robbery of Patricia McDonough. Smith, a blue-collar worker who followed up the robbery with obscene phone calls to the victim, is now serving a six-year sentence in the Maryland Correctional Institution in Hagerstown.

In another pen-register case just a year ago, the Supreme Court ruled that the device isn't covered by a 1968 federal wiretapping law because it doesn't "intercept" phone conversations and, in fact, doesn't indicate even if a call is completed.

Maryland Attorney General Francis B. Burch and Smith's lawyer, Howard L. Cardin, agree that the Maryland case directly raises the issue of whether pen-register surveillance is subject to the Fourth Amendment protection against unreasonable searches.

"What it basically comes down to is, does a person have the right to make calls to other people without the world knowing who he is calling?" Cardin said.

The case began 2 1/2 years ago when Patricia McDonough, returning to her home in Baltimore, saw a man changing a tire. As she neared the house, she was grabbed from behind by a man who wrenched away her purse and fled -- but not before she got a full-face view of him.

She described him and his car to police. Later, she got first one threatening and obscene phone call from a man who said he was the robber, then a series of such calls.

Nine days after the robbery, the caller phoned to ask McDonough to step outside so he could see her. She went out to her porch and saw the car go slowly by.

The next day, near McDonough's home, Smith stopped police officer Kenneth Lucas to get help in opening a locked door on his car. Lucas took down the license number and traced the car's ownership to Smith.

At the request of police, the phone company installed a pen-register in the office that serves Smith's home and almost immediately detected a call to McDonough.

With that, officers got a search warrant, entered Smith's home, found a phone book with a turned-down page listing McDonough's phone, arrested him, and put him in a lineup from which McDonough picked him out as the robber.

In pretrial proceedings, Smith unsuccessfully sought suppression of the pen-register evidence and of the lineup identification.

Rejecting his arguments, the divided Maryland Court of Appeals held "that there is no constitutionally protected reasonable expectation of privacy in the numbers dialed into a telephone system..."

Consequently, the court said, "no search within the Fourth Amendment is implicated by use of a pen-register installed at the central offices of the telephone company."

The dissenters contended that the use of a pen-register is, constitutionally, a search requiring the police, in advance, to get either a search warrant or a court order.

Agreeing in the successful petition for high court review, Smith's lawyer, Howard Cardin, said the pen-register is "a secret invasion of an individual's privacy."