Det-Sen. Sgt Dean Bailey said police believed Shawn Adam Newton could be carrying a firearm and warned people not to approach him.
Sen. Sgt Bailey said police who were investigating the discovery wanted to speak to Mr Newton, 42, and called for information to help track him down.
He has been described by police as light-skinned, 186cm tall, with a medium build, short dark hair and brown eyes.
The hunt came as the dead woman was identified as Rebecca Jane Gascoigne, 35, from Scarborough, who is a mother of three.
Another man, aged 49, who is alleged to have been driving the Mitsubishi Lancer when the body was discovered, was helping police with their inquiries.
Meanwhile, police continued to search a property at Abbett Street, Scarborough.
Sen. Sgt Bailey said the dead woman, the driver of the car and Mr Newton were all known to each other, but could not say how.
“He is considered extremely dangerous and the public are warned not to approach him as he is in possession of a firearm," he said.