Three people were bludgeoned to death with a barbell yesterday inside the basement of a South Bronx apartment building, authorities said.

Authorities identified the victims as a 56-year-old woman and her 36-year-old son, who lived together in the building on Hall Place in Morrisania. They said a third victim was the building’s 60-year-old assistant superintendent, whom they believe may have interrupted the attack on the other victims.

Last night, police sources said investigators were looking for the woman’s boyfriend, who recently finished a prison sentence. Police said they do not know what motivated yesterday’s murder.

Police said the victims were discovered around 11:50 a.m., after a maintenance worker in the building found the superintendent unconscious in a basement apartment. Officers responding to the 911 call canvassed the building, and in another basement apartment they located two additional victims — identified by neighbors as Gloria Valdez and her son, Carlos.

Those familiar with the investigation said officers entered a gruesome scene. All three victims suffered severe head trauma, and investigators located a bloody barbell they believe was used in the murder. Police said the woman and her son died at the scene, while the superintendent was taken to St. Barnabas Hospital, where he was pronounced dead.

A spokeswoman for the Medical Examiner’s Office said autopsies for the three are scheduled for today.

On the street outside the apartment building yesterday, those who knew the woman and her son described them as neighborhood fixtures. Several said they often saw Carlos Valdez practicing karate with children in the park across the street from his home, or walking his pet Chihuahua.

Those who knew Gloria Valdez said she recently ended a relationship with her boyfriend. “She told me she’s been having problems with him,” Yvonne Fraiser, 47, said. “They broke up on bad terms.”

Yesterday afternoon, investigators converged on the six-story, brick building located in the Hunts Point section of the South Bronx that is known, in part, for high crime rates. According to the police department’s CompStat report of crimes through October 15, there were 10 murders so far this year in the 41st precinct, where yesterday’s triple homicide occurred. That is up from six murders at this time last year. Citywide, police reported 441 murders so far this year, compared with 429 at this time last year.

Even in the beleaguered Bronx neighborhood, neighbors expressed shock at the homicide.

“I’ve lived here all my life. It’s shocking,” a neighbor of the victims, Carmen Melendez, 38, said.

The city’s last triple-slaying occurred in June 2003, when three members of a Queens family were shot and killed by a woman and her accomplice, whom authorities said were searching for drugs. Before that, in 2002, a couple and one of their neighbors were killed by a burglar on the Lower East Side.