A man in Ohio has been fatally shot by police while, his family said, he was cleaning out his dead grandmother's apartment.

Joe Frasure was shot on Monday in the town of Wyoming and died in hospital on Tuesday.

Police have said officers believed the 28-year-old was a burglary suspect and that he drove a van at them.

However, his family has disputed the authorities' account and want bodycam footage of the incident to be released.

Police have said that they arrived at a residence on Durrell Avenue just after midnight on Monday following reports of a possible burglary.

There they found two men at the back of the house and said that Frasure didn't respond to the officers' commands and tried to flee in a minivan. It is unclear whether Frasure was in the van when officers arrived or got in afterwards.

"The minivan reversed at a high rate of speed, before hitting a tree, at which point the vehicle accelerated rapidly at our officers," said Wyoming Police Chief Brooke Brady.

She added that police fired four shots at the van and that Frasure was hit. The van then hit the building.

Ms Brady said the officers then pulled Frasure from the car and performed life-saving care on him before he was taken to hospital.

The county coroner has listed Frasure's cause of death as a police-involved shooting, WLWT news reports.

The second man at the back of the house has been identified as Frasure's father. According to WCPO 9 News, Wyoming police have said that he was no longer "sought by police", but would not provide any other details.

Frasure's family held a protest outside the Wyoming police department on Wednesday, demanding justice.

His brother has alleged that Frasure was shot in the back of the head, WCPO reports, in an apparent contradiction of what the police have said happened.

"I want to know why they killed my brother," he said. "My brother was a father, a brother, a son, a family member. A loving friend."