Officers got reports of a Peugeot 206 being driven erratically in Coleraine around 20:00 BST last night.
They saw the vehicle on the Cromore Road in the town and began a pursuit. The car crashed on the Millburn Road a short time later.
Five people were taken to hospital, and two men, aged 26 and 23, and two women, aged 23 and 20, were later arrested.
They remain in custody.
A fifth person is still in hospital, but is not believed to have serious injuries.
PSNI chief inspector Mark McClarence said reports suggested the car had "allegedly [been] involved in theft across the Derry, Limavady and Coleraine areas from around 7pm".
He added: "The vehicle was spotted by police and was pursued by suitably trained officers."
The Police Ombudsman's office was informed about the incident but has since decided that no investigation was necessary.
Four people have been arrested after a car crashed as it was being followed by police in County Antrim.