Police have spoken to potential witnesses to the fracas which cost Jeremy Clarkson his job at the BBC, saying they "have a duty to investigate" what happened.
Clarkson's Top Gear contract has not been renewed by the BBC after an internal investigation found he attacked show producer Oisin Tymon after an angry and lengthy tirade in a hotel in the county.
The 54-year-old presenter today called on people to leave Mr Tymon alone " because none of this was his fault".
The producer has come under huge abuse from trolls on Twitter, including receiving death threats.
North Yorkshire Police said they had been contacted by " concerned members of the public", asking what action they were taking in relation to Clarkson.
The force said in a statement: "N o-one who was present at the hotel during the incident came forward to report an offence to the police. Nonetheless, we have a duty to investigate where we believe an offence might have been committed, and that is what we have been doing with this case.
"We have already spoken to some people who were in the hotel at the time, but there are still others we need to speak to, who could help us to determine exactly what happened.
"Also, as is usual in these circumstances, we have made contact with Mr Tymon through his lawyers, to ask him to speak to us so we can ascertain how he wishes to pursue this matter.
"When these routine inquiries are completed, we will be able to assess whether or not further action needs to be taken from a police perspective.
"Meanwhile, we'd like to reassure the public that the matter is in hand, and we dealing with it responsibly and proportionately."
Returning to his west London home today, Clarkson refused to answer when asked if he was worried about being arrested.
Instead, he said: "All I would like to say is ... I wish people would leave Ois alone because none of this was his fault."
When the star was asked what he would like to say to fans who may be upset about him leaving the show, he replied: "Everybody's upset."
Clarkson faces an uncertain future as reports suggest that his co-stars, James May and Richard Hammond, may leave the show alongside him.
All three presenters' contracts run out at the end of this month.
BBC director-general Tony Hall has made it clear he wants the programme to continue but May said he was considering his position and Hammond declared it the "end to an era".
The BBC confirmed that Clarkson's contract would not be renewed after its investigation found the presenter's attack on Mr Tymon left him needing hospital treatment.
As for Clarkson's broadcasting future, two major companies - Sky and Channel 4 - are understood to have ruled out working with him, while ITV would not comment on "a BBC issue".
Chris Evans leads the betting as favourite to take over at the show even though he has ruled himself out on more than one occasion.
In his last column for the show's magazine, Clarkson hit out at Top Gear's detractors and challenged them to make their own rival show.
He wrote the piece before the attack on Mr Tymon but it was only published today.
In something of a coincidence, the star, who may be mulling over ideas for a new motoring show to take to another broadcaster, told unhappy viewers to "get off your arse and help yourself".
He told the programme's critics, who he called "hopeless worms", that instead of moaning that Top Gear should "go back to the days when it reviewed cars" they should try making their own show.
In the magazine, on sale today, the broadcaster said there was plenty of room in the market for another car show.
"You have Top Gear and Fifth Gear and Chris Harris and, er, that's it. So, in order to shine, all you have to be is better than Captain Slow, a midget, a pensioner, an orangutan and a monkey. Which isn't hard," he said.