An orange Vauxhall Corsa failed to stop while driving along Edinburgh Road in Perth at 1.55pm on Saturday.
Officers followed the car before it crashed on the A90 near St Madoes, around six miles away.
No police vehicles were involved in the crash.
The car’s four occupants were taken to Ninewells Hospital in Dundee, including the two girls aged 14 and two boys – aged 16 and 14.
The boys were treated for minor injuries.
Sergeant Michelle Burns said: “Our enquiries into this incident are ongoing and we would urge anyone who may have seen the Vauxhall Corsa or the police vehicles in Perth, on the A912 through Bridge of Earn or on the A90 are asked to come forward.
Police are keen to speak to anyone with dashcam footage.
Information can be passed to police by calling 101, quoting incident 2040 of 20 February.