He was injured after allegedly taking part in an armed robbery in Meadow Close, Stratford-upon-Avon, on Thursday night with another man.
A man delivering a takeaway meal was threatened with a knife and had his car stolen, police said.
It then overturned on Red Hill, Billesley. Police, who came across the crash, arrested two men, one of whom ran away and was hit by two vehicles.
The Independent Police Complaints Commission has been informed of the incident, in line with standard procedure.
Lost control
The delivery man had been confronted by two men in hooded tops and one of them had threatened him with a knife, police said.
He suffered a slight injury but did not need hospital treatment.
During the incident, a blue Volvo 850 was stolen and was driven on the A46 towards Alcester. The driver is believed to have lost control of the car near to The Stag pub.
One of the men was hit by two vehicles as he crossed the road. He was taken to Warwick Hospital with suspected leg and spinal injuries but was released after treatment.
Two men are being held in custody at Leamington Spa in connection with the robbery and the two road incidents.
Anyone with information is asked to contact Stratford CID or Crimestoppers.
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