The driver sped off south on Broadway and got on westbound I-94, according to a news release.
The officers briefly lost sight of the car before discovering the crash at the Colfax Street bridge, he said.
The 20-year-old Matteson, Illinois, woman riding with the driver was killed instantly when he rear-ended a semitrailer, Martinez said. An infant, who was in a car seat, also was pronounced dead at the scene, he said.
Neither of the crash victims have been identified by officials as of Friday night.
Indiana State Police assisted with a crash reconstruction investigation and determined the driver of the Audi lost control and rear-ended a semitrailer in the right lane, Sgt. Glen Fifield said.
“After striking the trailer, the Audi spun across all lanes and drove into the median wall,” Fifield said. “After hitting the wall, the Audi then continued back across the lanes in front of the same semi that it had rear-ended and was struck on the passenger side by the front of the semi.”
The Audi came to rest wedged under the front bumper of the semi, he said.
The woman suffered fatal injuries during the initial impact with the trailer and was ejected, Fifield said.
UPDATE: Driver identified in crash that killed infant, woman on I-94, sheriff says