Four days after the allegations were aired by News Corp, then by Channel Seven - the organisation the woman works for - police confirmed to Fairfax Media that they have taken over the investigation.
Victoria Police said in a statement that they are probing reports a woman was threatened by a man at a Chapel Street restaurant about 9.42pm on Saturday.
"The incident was not initially reported to police," a spokeswoman said.
"However, police are now aware of the incident and have identified the victim is a woman from Sydney. The investigation remains ongoing, therefore no further comment will be provided."
The Tigers star, who was reportedly intoxicated after spending the day at Stereosonic music festival, was dining at Windsor restaurant Mr Miyagi on Saturday night.
He allegedly became angry after the 30-year-old woman told him to calm down.
She claimed Martin raised the chopsticks above her eye and threatened to stab her before he slammed his palm against a wall above her head.
"He reacted extremely angrily, very very agitated, began swearing at me, standing over me physically, it was extremely intimidating," the Sydney woman, identified as "Tracey", told Channel Seven.
It is believed the woman first complained to the Richmond Football Club before AFL integrity investigators became involved.
Fairfax Media understands a number of independent witnesses interviewed by the AFL and Richmond prompted the league to refer the matter to police with the view that the matter was better investigated
by the state's law enforcers.
It is believed that several witnesses who saw Martin confront the woman have played down what has been reported as a vicious and threatening verbal attack.
Unwilling to take any action against Martin until all the facts had been fully uncovered the view of Richmond integrity officer Steve Wyatt and Brett Clothier's AFL team was that the prudent option was to place the matter in the hands of police.
Both the AFL and the Tigers refused to comment on Thursday night on the new witness statements but those statements have reportedly placed Martin's behaviour, while still unacceptable, in a more favourable light.
Martin has apologised to the woman.
He said in a statement released by the club late on Monday afternoon: "Regrettably, I was intoxicated and that, in itself, is completely unacceptable.
"I do, however, take responsibility for my behaviour and I am deeply embarrassed.
"If anything I have said or done has caused anyone to feel threatened, then that is totally inappropriate."
Fairfax Media has been told by sources close to the investigation that closed circuit television footage could not be recovered from the restaurant. The restaurant could not be reached for comment on Thursday.
The head of the AFL Players Association Paul Marsh said earlier on Thursday the group will help Martin through the allegations.
Speaking on the steps of State Parliament to launch the "not on our watch" campaign against violence, Marsh was asked if Martin should receive a tough punishment to send a message that this type of behaviour was unacceptable.
"That issue is still under investigation," Marsh said.
"There is no excuse for violence. In saying that, if we have a player in a situation like Dustin has been alleged of, we will still help and support him. It is about changing behaviours long term."