Jeremy Clarkson faces the possibility of police action after the "unprovoked" attack on a colleague.
A BBC report found the 30-second attack, which was only stopped when a witness intervened, was accompanied by a volley of verbal abuse so loud it could be heard throughout the hotel where the programme's crew were staying.
Jeremy Clarkson faces a police probe
It said Mr Tymon, who was left with a split lip after being struck by Clarkson, "believed that he had lost his job" following the attack and drove himself to a "nearby A&E department for examination".
A spokeswoman for North Yorkshire Police said the force had asked the BBC for its report on the incident which happened at a hotel in the county.
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She said: "The information will be assessed appropriately and action will be taken by North Yorkshire Police where necessary.
"It would not be appropriate for North Yorkshire Police to comment further at this time."
Top Gear producer Oisin Tymon drove himself to A&E with a bloodied lip after the altercation
Mr Hall, who said he had met and spoken to both men, said the BBC needed "distinctive and different voices" but not "at any price".
He said: "Common to all at the BBC have to be standards of decency and respect.
"I cannot condone what has happened on this occasion. A member of staff - who is a completely innocent party - took himself to Accident and Emergency after a physical altercation accompanied by sustained and prolonged verbal abuse of an extreme nature.
Clarkson updated his Twitter bio on Wednesday to reflect the fact he'd been sacked
"For me a line has been crossed. There cannot be one rule for one and one rule for another dictated by either rank, or public relations and commercial considerations."
The BBC investigation found that Mr Tymon was "subject to an unprovoked physical and verbal attack by Jeremy Clarkson".
It said: "Verbal abuse was directed at Oisin Tymon on more than one occasion - both during the attack and subsequently inside the hotel - and contained the strongest expletives and threats to sack him. The abuse was at such volume as to be heard in the dining room, and the shouting was audible in a hotel bedroom."
Mr Hall said "no blame" was attached to Mr Tymon, who, he said, "behaved with huge integrity throughout" and the producer himself paid tribute to the man who attacked him.
Mr Tymon said: "I've worked on Top Gear for almost a decade, a programme I love. Over that time Jeremy and I had a positive and successful working relationship, making some landmark projects together. He is a unique talent and I am well aware that many will be sorry his involvement in the show should end in this way."
Clarkson and his co-hosts, James May and Richard Hammond, were scheduled to take part in four live Top Gear shows in Norway this week, but it was announced on Sunday that they had been postponed.
All three men's contracts run out at the end of this month and Hammond and May's future is still unclear, though Mr Hall said the BBC wanted to "renew" the show for next year.
Speaking outside his home, May said Clarkson's departure was a "tragedy".
He said: "I'm sure Top Gear will continue in some way. It existed before us and it has been reformatted several times."
Asked if he will stay at Top Gear, May said: "Erm, well, I don't want to talk about that too much but I think we are very much the three of us as a package. It works for very complicated reasons that a lot of people don't fully understand. So that will require a lot of careful thought."
Hammond said he was "gutted at such a sad end to an era" after Clarkson's sacking. He added: "We're all three of us idiots in our different ways but it's been an incredible ride together."
The BBC declined to comment on the future of the other two men.
Clarkson changed his Twitter profile to: "I used to be a presenter on the BBC2 motoring show Top Gear."
Clarkson's next step is unknown but it is understood at least one major broadcaster - Sky - has ruled out signing him up.