One of the boys is 15 years old and was arrested on suspicion of dangerous driving.
The officers spotted the car in Holbrook Lane, Coventry and attempted to stop it however the vehicle fled.
The car stopped in Bedworth and the occupants ran off.
Officers located one suspect on Coventry Road and another on Longford Road.
A 15-year-old boy from Coventry was arrested on suspicion of dangerous driving, driving under the influence of drink or drugs, burglary, driving without a licence or insurance, failing to stop, aggravated vehicle taking and theft of a motor vehicle.
A 17-year-old boy from Coventry was arrested on suspicion of theft of a motor vehicle, dangerous driving, failing to stop, driving while under the influence of drink or drugs, and burglary.
Both boys have since been released under investigation while enquiries continue.
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