Officers discovered the woman’s body at a house on Samman Road in Beverley in the early hours of Monday July 25 after receiving reports of concern for safety.
A man was reported to have left the address in Beverley in a Volkswagon Polo at around 6am.
The car was later seen by police officers on the A1035 between Seaton and Hornsea and a "short" police pursuit ensued.
The Polo was in collision with a Ford Transit van, at around 6.30am. The driver of the Polo was pronounced dead at the scene.
The man driving the Ford Transit van was taken to hospital with serious and potentially life-changing injuries and remains in hospital.
The incident has been referred to the Independent Office for Police Conduct to be independently reviewed as there had been a police pursuit.
Detective Chief Inspector Curtis said: “The woman’s family have been informed of her death and the investigation into her murder and are being provided support by specially trained officers.
“The man’s family have also been informed of his death and specially trained officers are in contact with them offering support.
“Specialist Roads Policing Officers are in contact with the driver of the Ford Transit and their family to offer support and updates in regard to the investigation.
Anyone who has information and has not already spoken to police should call 101 or anonymously to independent charity Crimestoppers on 0800 555 111