Police were driving in Providence Hill, Bursledon, when a vehicle drove off at speed away from officers at around 12.21am on Tuesday morning.
The vehicle later collided with some hedges at the junction of Portsmouth Road and Wrights Hill in Sholing, before three occupants of the vehicle were detained by officers, including a 17-year-old boy who left the area on foot.
The boy was detained by the police dog unit.
He, and a 20-year-old man, were subsequently taken to hospital, Hampshire Constabulary confirmed.
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In a statement, a spokesperson for the force said: “The 17-year-old remains in hospital at this time for treatment to an arm injury, however he has been arrested on suspicion of dangerous driving and possession of an offensive weapon, namely a flick knife.
“The 20-year-old man has been discharged from hospital and is currently in custody having been arrested on suspicion of dangerous driving, failing to stop, and theft of a vehicle.
“The third vehicle occupant, also a 20-year-old man, was arrested on suspicion of dangerous driving, failing to stop, drug driving, driving whilst unfit through drink, burglary and theft of a vehicle. He remains in custody at this time.”