Police previously said the pursuit began shortly before 17:30 BST on Birmingham Road when officers attempted to stop the Audi, but the driver failed to pull over.
The crash happened about 15 minutes later, the force said.
The Ford driver, initially reported to be in her 70s, was taken to hospital along with another woman, who had been a passenger in the Ford.
West Midlands Ambulance Service said the second woman had suffered serious injuries, but they were not thought to be life threatening.
Injuries to another patient from the Ford were not believed to be serious.
After failing to stop, the Audi made off in the direction of the A46 before travelling back towards Stratford on the A439.
A number of other cars were damaged during the pursuit, police said.
Warwick Road was closed on Monday from the Marraway roundabout to its junction with Ingon Lane and Sand Barn Lane, with the stretch remaining shut on Tuesday morning.
Manuela Perteghella, Liberal Democrat MP for Stratford-on-Avon, said on Tuesday the incdent was "incredibly tragic".
"My thoughts are with the families of all those impacted. We must now let the investigation take its course."
The IOPC is asking anyone who may have footage of the Audi or the pursuit to contact them.

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