Sgt. Nancy Higgins said Tuesday that violent crime investigators are looking into whether Monday night's crash was a suicide-homicide.
The victims were identified early Tuesday by the Cook County medical examiner as Shirley Combest, 33, her daughter, Shaniqua, 8, and her son, John, 6. They were residents of the South Side.
The car veered off Lake Shore Drive near Buckingham Fountain, went slowly down some steps and paused for a moment before it suddenly accelerated and went into Monroe Harbor, police and witnesses said.
Combest's mother told WBBM her daughter had been depressed over the death of an older sister in an auto accident earlier this month, and her uncle's death from cancer earlier this year.
Police said even before Shirley's sister died, she was under a doctor's care and taking medication for depression.
Two police officers who went in the water to attempt to rescue victims were also taken to the hospital after suffering the effects of exposure. Both were reported in good condition.
Police diver Milton Storey said the car still had its headlights on as it sat on the bottom in the cold, murky waters. He said the divers had to break a window to get into the vehicle.
"There was zero visibility," Storey said. "You couldn't see the hand in front of your face."
The silver 1999 Nissan Altima was pulled from the lake at about 11:30 p.m.
Combest's mother, Ruthie Mae Combest, 68, told WBBM she's trying to cope with losing two daughters and two grandchildren in one month.