Excessive speed and bald tires likely caused a stolen car being followed by a state trooper to lose control Sunday night and plow into an icy sump pond in Albertson, killing three men inside, State Police said Monday.

“The vehicle was attempting to make a left-hand turn at a high rate of speed,” said State Police Maj. David Candelaria, commander of Troop L in Farmingdale. “ . . . It wasn’t 100 miles per hour or anything like that, but that neighborhood is a 30-mile per hour zone, so with a little bit of icy roads and you’re going beyond 30 miles per hour and you try to make a hard left hand turn, you just slide right off the road.”

Candelaria said the investigation by the agency’s Collision Reconstruction Unit is ongoing but several of the stolen Honda sedan’s tires “were almost bare, bald.”

State Police on Monday identified the three victims as Donald Farr, 51, of Westbury, Adolph Ford, 46, of Roosevelt, and Joan A. Sanjuan, 29, of Central Islip.

All three were pronounced dead at a hospital, police said.

Sanjuan’s mother, Alexandra Sanjuan, said she was too pained to speak about her son. According to his Facebook page, Joan Sanjuan graduated from Queens Vocational High School and worked as a canvassing coordinator at Make the Road New York, a social justice organization with an office in Brentwood.

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“At this point I don’t know what happened,” said his distraught mother. “We’re waiting for the investigation report. . . . The only thing that I know is that my son is dead.”

Walter Barrientos, the Long Island coordinator at Make the Road, confirmed Sanjuan had worked with the group a few years ago. Barrientos said Sanjuan’s mother works at the organization.

“It’s been a day of mourning since we learned about the accident last night and we have been doing everything we can do as an organization to support her and the family to get through this difficult time,” Barrientos said.

Family members of Farr and Ford could not be reached for comment Monday.

Candelaria said investigators are still trying to determine who stole the car and the relationships among the three men. It was unclear who was driving at the time of the crash, he said.

Just before 6 p.m. Sunday, the car crashed through a fence and into the sump pond on the northeast corner of I.U. Willets and Searingtown roads in a residential area, police said.

Shortly before the crash, authorities said, the car passed a marked state police cruiser parked on the eastbound side of the Northern State Parkway. The trooper inside was alerted through the cruiser’s license plate reader that it was a stolen 2010 Honda, Candelaria said. The trooper followed the car, but did not activate any lights or siren and called for backup, Candelaria said.

“This trooper was not in a pursuit,” Candelaria said. “We follow suspicious vehicles all the time. He was not in a pursuit.”

Candelaria would not identify the trooper, but said he is a 14-year State Police veteran and previously served in the NYPD and Marine Corps.

With the trooper following, Candelaria said the car exited the parkway onto southbound Shelter Rock Road before making a left onto eastbound I.U. Willets Road. The Honda suddenly accelerated, and the trooper said to dispatch: “I think he spotted me.”

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The Honda then “illegally” passed several eastbound vehicles and attempted a left turn onto northbound Searingtown Road, but the driver “failed to navigate the left turn” and the car crashed through the fence, flipped over, and landed in the frigid water.

Candelaria said the trooper immediately called for help, with Nassau police and the Albertson Fire Department responding within minutes.

“He was screaming, ‘Come on guys, get out, it’s only a stolen car, get out of the car, get out of the car,’ ” Candelaria said of the trooper who followed the Honda.

Within minutes, the trooper said over the radio that the car was submerged.

Nassau Police Officers Michael Iannarelli and Robert Petry, of the department’s Emergency Service Unit, donned special diving suits in the icy, 10-foot-deep water Sunday night as they tried to save the men.

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Both officers said they never heard screaming or calls for help.

One of the Honda’s occupants was just below the water’s surface, Petry said.

Iannarelli grabbed the man and handed him off to Petry, who got him to the shore. The man was unconscious when pulled from the water, Petry said.

“We hooked the chain onto the car, pulled the car to shore, flipped it over, pulled it up and we had to get the two others out because they were trapped in the vehicle,” Petry said. “It was definitely subfreezing, without a doubt there was ice on top of the water. A lot of silt in the water, sticks, rocks, debris, everything else, so you couldn’t see anything.”

Iannarelli added: “Once we able to get the car out of the water, we were able to get them out pretty quickly.”