Officers were contacted by the North West Ambulance Service at 2.44pm yesterday (January 13) following the collision on the city’s Ullswater Road.
A pedestrian – a man, 46, of Carlisle – was taken to the Royal Victoria Infirmary in Newcastle with a head injury.
He was today in a critical but stable condition.
A man, 30, suspected of being the driver, was arrested on suspicion of assault causing grievous bodily harm. A woman, 32, was arrested on suspicion of assisting an offender.
Both are in custody today.
Anyone with information should call police on 101, referring to incident 124 of January 13.