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Police were not notified of the shooting of the son of Chicago Teamsters union official Daniel Ligurotis Sr. until about 90 minutes after the father fired the fatal bullet, law enforcement officials said Thursday.

The timing of telephone calls to police has become a critical factor in the investigation to determine whether criminal charges should be brought against the father, or whether there was an attempt to influence the police investigation of the shooting, authorities said.

Telephone calls made from the scene of the shooting, the headquarters of Teamsters Local 705, 300 S. Ashland Ave., are being reviewed by investigators to establish whether high-ranking police officials were contacted about the incident before it was reported to 911 emergency dispatchers, law enforcement officials said.

Meanwhile, no charges have been filed against the father.

Ligurotis, 63, spent Thursday afternoon at his Westchester townhouse, exhausted and grieving while helping to arrange the funeral of his only child, according to close associates.

Earlier in the day, after retelling his version of events to authorities for nearly 13 hours, Ligurotis was released from a West Side police station. The tall, powerfully built Ligurotis told investigators that he had fired a fatal shot at his adopted son in self-defense. Police believe the two were alone when the incident took place Wednesday morning in a basement exercise room.

Police and prosecutors continued to sort through a host of unanswered questions about the incident, including the delay, the relationship between father and son and what role a retired police official and current Teamsters business representative played in reporting the incident to police.

”It is a continuing investigation; further comment now would be inappropriate,” said a spokesman for Cook County State`s Atty. Jack O`Malley. The spokesman, Andy Knott, added that O`Malley had assigned his chief deputy state`s attorney, Patrick O`Brien, to oversee the inquiry.

The case is a sensitive one to O`Malley because a decision to bring charges against a powerful union official could hurt him politically.

Some police officials were more candid.

”There are a lot of things that don`t fit,” said Lt. Larry Williams, acting commander of the Harrison Area detectives, the division responsible for investigating the shooting.

”It takes time to develop the evidence,” said Harrison Area Sgt. William Rooney. ”The crime lab is working on it. Until they can give us the scientific results, we can`t do anything with it. . . . There were only two people down there.”

Fingerprints found on the pistol reportedly used by the son were described by police as ”smudged,” but an effort to enhance them was continuing, police said.

The shooting took place between 8 and 8:30 a.m. Wednesday, but it was not reported to authorities until about 9:40 a.m., according to Rooney and other law enforcement officials.

Sources close to the investigation said they have received information that police were initially notified of the shooting not through a 911 emergency call, but through a telephone call to police headquarters from retired Deputy Police Supt. John Killackey, now a $49,390-a-year business representative of Local 705.

Killackey could not be reached for comment.

Killackey accompanied Ligurotis to the police interrogation and remained with him.

After a reporter inquired about Killackey`s presence, a uniformed policeman was instructed to keep the media out of the interrogation area.

The time delay also has become a focus of the investigation in part because by the time investigators began attempting to question union associates and relatives about the incident, some of the individuals had already consulted lawyers, according to authorities.

Teamsters lawyer Rory McGinty, who represents Local 705, said any delay by Ligurotis in notifying police of the shooting was due to ”shock.”

”He (Ligurotis) was in shock, and that is what the state`s attorney`s office will conclude,” McGinty said Thursday outside the elder Ligurotis`

home.

”Dan is fully cooperating” in the investigation, said Sherman Carmell, a veteran Chicago labor lawyer and longtime friend of the elder Ligurotis`. He represents Teamsters District Council 25, headed by Ligurotis.

”He acted appropriately,” McGinty said. ”It is a horrible tragedy, but there was no crime committed. We are not trying to hide anything.”

The fatal shooting occurred, the elder Ligurotis told police, after he went to the basement exercise room with his son to discuss ”family affairs,” according to Deputy Police Supt. John Townsend.

Ligurotis told investigators that he fired a handgun after his son had threatened him with his own gun, a .25-caliber pistol, police said. The bullet entered the victim`s head just above the left ear and exited through his forehead above the right eye, police said.

The shooting appeared to contradict what was in many ways an intimate relationship between Ligurotis and his son.

The two lived side by side in identical upscale Westchester townhouses. Prior to moving into the townhouses slightly more than a year ago, the two families lived together under the same roof elsewhere in the west suburb. Friends said the elder Ligurotis had always wanted to live near his son and two grandsons, whom he adored.

The closeness of the relationship was most evident in their joint labor union activities.

The elder Ligurotis holds a number of policy-making positions within the local and national union and is a candidate for secretary treasurer in the national union in upcoming elections. He receives annual salaries totaling $411,427.

With the full support of his father, Ligurotis Jr., 36, was handed a succession of good-paying jobs within the union local. The son was paid $90,329 a year as a trustee of Local 705. On top of that, he also received an annual salary of $19,400 as a union legal liaison, records show.

Despite the appearance of success, Ligurotis Jr. had battled what family friends and union associates described as a chronic abuse of drugs and alcohol that dated to his teens. In recent years, Ligurotis Jr. was in and out of drug rehabilitation centers, never completing a program, friends said.

On June 6, Ligurotis Jr. was arrested by Westchester police after a car chase following a domestic disturbance at his home. A friend of the family contacted authorities and said she was worried about the well-being of the younger Ligurotis` family. She requested police and an ambulance be sent to the home.

A police report of the domestic disturbance said Ligurotis Jr. returned to his house while police were there and was arrested on misdemeanor charges. On July 18, he was fined $50 in court for disobeying a police officer, according to Westchester police records.