SAN JUAN, P.R., - The United States Justice Department has been investigating members of the Puerto Rican police force in connection with murders, kidnappings, narcotics trafficking and the theft of $1.3 million in gold, according to Puerto Rican officials close to the inquiry.
Senior law-enforcement officials in Washington said the investigators had found evidence of ''broad and significant police corruption'' and are now presenting it to a Federal grand jury here.
The inquiry, covering the last two years, was carried out by a special 15-member Justice Department task force with the cooperation of the Bureau of Special Investigations of the Commonwealth's Department of Justice. It began, the Federal officials said, as an investigation of the slaying of a murder witness, and was initially requested by Puerto Rico's Governor and Police Superintendent.
On Dec. 15 members of the task force and agents of the Federal Bureau of Investigation entered police headquarters with subpoenas for the records of 30 current and former officers. Most of the subpoenaed records were those of members of the Criminal Investigation Corps, the detective division. Autopsy records have also been subpoenaed. Change in Reputation
For decades, the Puerto Rican police had a reputation for being inefficient but honest. In the last decade reports of ''death squads'' and of detectives trading in narcotics and stolen merchandise proliferated, but no major indictments resulted.
The Justice Department twice investigated the Police Department in connection with the July 25, 1978, shooting deaths of two Puerto Rican separatists. But Federal officials said the inquiries, which were closed in May 1980 and January 1981, did not produce enough evidence to prosecute anyone under the Federal civil rights laws.
Early last September, Alejo Maldonado, a detective holding a rank equivalent to major, was arrested and charged with masterminding the kidnapping of the son of a San Juan jeweler.
The kidnapping victim, Mario Consuegra, a 22-year-old Cuban exile, was released unharmed after his father, Francisco Consuegra, paid $244,000 in cash and jewelry for his release.
The elder Mr. Consuegra had notified the F.B.I. of the kidnapping, and Federal agents arranged with the police to trap the kidnappers when they went to collect the ransom. Although most of the kidnappers escaped with the money, the authorities said, Mr. Maldonado was followed and arrested near his home in Caguas, 18 miles south of San Juan. Tape on an Abduction
Five others, none of them police officers, were subsequently charged in the kidnapping. In the investigations, the F.B.I. found among Mr. Maldonado's possessions a tape recording that, according to the indictment, was used in another, unreported, abduction, that of Julio Cortes Jr., who was freed unharmed after a $200,000 ransom was paid.
In recent months some Puerto Rican newspapers have speculated that some local killings, including murders of suspected racketeers, had been carried out by members of the Police Department to cover up their own wrongdoing.
In a news conference Dec. 16, the day after the Federal investigation came to light, Gov. Carlos Romero Barcelo and Police Superintendent Desiderio Cartagena disclosed their role in the inquiry. They said they had sought the help of the Federal authorities in investigating possible police corruption after a 19-year-old girl who had witnessed a murder was killed while in police custody in May 29, 1980.
The victim, Griselle Gonzalez Ortiz, known as Jessica, was kept in protective custody in police headquarters for several months after she agreed to testify as a witness to the murder of a man who had witnessed another murder. Bullet Hole in Police Car
She was found shot to death in a rural area outside San Juan. Shortly thereafter, a police squad car was found to have a bullet hole in the door, from a shot fired inside the vehicle, and bloodstains on the seats and carpet matched Miss Gonzalez Ortiz's blood type.
It has not been made known whether the investigating authorities believed Miss Gonzalez Ortiz, who was pregnant, had been murdered because of a personal involvement with a detective in the security detail or to silence her as a witness.
Although several officers suspected of the murder have resigned, no charges have been filed. Sources close to the investigation in Puerto Rico indicated that indictments may be handed up soon.
Meanwhile, another detective, Julio Andrades, who held a rank equivalent to lieutenant, was permitted to resign while being investigated by the Federal Drug Enforcement Administration and the Police Narcotics Division. Sources close to that investigation said he was suspected of participating in a multimillion-dollar marijuana and cocaine airdrop on Puerto Rico's south coast.
According to the Puerto Rican law-enforcement authorities, the investigators also believe that several unsolved bank robberies were carried out by some members of the detective division, which has several hundred members.
In some of these robberies, investigators believe, the detectives made telephone calls to news organizations claiming responsibility for the robberies in the name of terrorist groups seeking Puerto Rico's independence.
The authorities are also said to believe that some detectives were involved in the theft of $1.3 million in gold from an Iberia Airlines plane on Sept. 19, 1981. Three crates containing the gold vanished on a stopover in San Juan on a flight from Madrid to Guayaquil, Ecuador.
A Puerto Rican law-enforcement official familiar with the Federal investigation said two police officers were strong suspects in the murder of Abraham Shafizadeh, a New York diamond salesman killed in Puerto Rico on July 28, 1977. Mr. Shafizadeh had reportedly planned to visit Hector Acevedo Ramos, a San Juan jeweler who has close personal ties to Mr. Maldonado, to collect some money owed him.
Neither the Shafizadeh murder nor the 1974 slayings in Puerto Rico of two other diamond salesmen, Leo Dershowitz of New York and Howard Block of Chicago, have been solved. When killed, each man was carrying more than $200,000 in diamonds, which were never recovered.

MANUEL SUAREZ, Special to the New York Times.