The European Parliament has reported UKIP MEPs Mike Hookem and Steven Woolfe to French police over their clash in September.
Hookem, who represents Yorkshire and Humber, which includes North and North East Lincolnshire, in the European Parliament and the now Independent MEP Woolfe were involved in the altercation in Strasbourg, which led to Woolfe being rushed to hospital with life-threatening injuries.
President of the European Parliament Martin Schulz has referred the matter to the French authorities, after a recommendation from the European Parliament conduct committee.
Schulz said: “Given the seriousness of the reported facts and their possible criminal implications, further evidence is needed to clarify that matter.
“As a result, I have decided to follow the recommendation of the advisory committee and I have referred this matter to the French authorities.”
Woolfe claimed Hookem “landed a blow” on him after the pair left a party meeting in the European Parliament building to settle a heated argument.
Hookem has repeatedly insisted that he did not strike Woolfe, describing the incident as a “tussle”.
Woolfe collapsed shortly after the altercation, spending three nights in hospital in Strasbourg.
On leaving hospital, Woolfe insisted that he had “received a blow” from Hookem, revealing also that he had made a police complaint about the incident.
Woolfe has since quit UKIP, claiming the party is “ungovernable” without Nigel Farage as leader.
Contradictory statements about the altercation were given to the European Parliament conduct committee, leading to them being reported to the authorities.
The MEPs also face sanctions for bringing the European Parliament into disrepute.
Possible punishments include them losing as much as £3,600 in allowances or being stripped of their voting rights for up to 10 days.
Hookem told the BBC: “Ever keen to stir the pot, the European Parliament president Martin Schulz and the leader of the EPP Manfred Weber have made defamatory statements in the chamber today claiming falsely that I punched Steven Woolfe.”