Stephen Walsh, 37, had been driving a Lexus car which was involved in a collision with another vehicle - possibly a gold-coloured estate car or car-derived van - in Newstead Avenue, Mapperley, sometime between 10pm and 10.30pm on Sunday.
It is believed Mr Walsh did not stop at the scene and instead drove to his home in nearby Blenheim Avenue, Mapperley.
A short time later a man turned up at his house and assaulted him, causing serious head injuries.
No weapons were seen.
The man, who is believed to have been the driver of the other vehicle in the collision, then left, saying he would return the next day to exchange insurance details.
Mr Walsh was found dead at around 5.55am the next morning.
A post-mortem examination was carried out yesterday and the initial report revealed he died of head injuries.
Further tests are being carried out.
So far the man has not reported the collision or come forward.
Detective Chief Inspector Hayley Williams, of East Midlands Special Operations Unit - Major Crime Nottinghamshire, said it appeared the assault was a spontaneous incident following the crash and there was no indication of any wider threat to the public.
She today appealed to the man to call the police as soon as possible.
She said: "I want to appeal directly to the driver. A man has died and his children and family deserve to know what happened. This will not go away. I appreciate you may be scared. I don’t think you planned this and I want to hear your side of the story. I have officers waiting to speak to you now and it would be much better if you come forward - because if you don’t, we will find you.
"I believe you have disclosed the crash - and possibly the assault - to others, possibly your girlfriend and mother. Please don't create difficulties for them by expecting them to cover up for you. I promise my officers will treat you fairly. By all means contact a solicitor and make arrangements to come in and talk to us."
Det Chief Insp Williams also appealed for witnesses to come forward.
"What we believe so far is that the person we are looking for is a white man in his 20s who was possibly driving a gold-coloured estate car or car-derived van. That vehicle will have some front offside damage," she said.
"I want to appeal to witnesses who know a friend, neighbour, colleague with such a vehicle to let us know, especially if it has accident damage or if they haven't seen it since Sunday night.
"If you are a garage who has been asked to do a repair on such a vehicle in the last 48 hours please let us know.
"My officers are standing by waiting to speak to anyone with any information about Stephen's death. Please do call us on 101, quoting incident number 100 of July 30, 2018, or Crimestoppers anonymously on 0800 555 111."