Police have spoken to witnesses who potentially saw the attack which led the BBC not to renew Jeremy Clarkson's contract.
The North Yorkshire force says it has a duty to investigate the incident.
But no-one's made a formal complaint.
The ex-Top Gear host has asked people to stop the online harassment of the producer he punched.
British Prime Minister David Cameron - a friend of Clarkson's - was asked about him losing his job.