The Wales and Northampton winger was injured against Leicester on Saturday.
TV replays appeared to show him lying motionless before he recovered to pass a mandatory pitch-side assessment.
Northampton said they had not had access to full television footage of the incident before allowing North to rejoin the action later in the match.
Rules dictate that any player with confirmed or suspected concussion should be permanently removed from a game.
Immediately after Saturday's contest, Northampton director of rugby Jim Mallinder said North, 24, had not been knocked out.
Premiership Rugby and the RFU have revealed that a Concussion Management Review Group (CMRG) met on Tuesday to assess the incident.
A statement said the group could decide to issue a warning or even recommend a misconduct charge against the club or an individual.
Wales international North fell heavily in a mid-air tackle that led to Leicester's Adam Thompstone being sin-binned.
He left the field for a mandatory head injury assessment by the club's doctor.
North was passed fit and returned to the action.
After the game, North said on Twitter he was "OK", adding: "I landed on my neck and was worried about it. Thanks to the medics for checking me out properly. I can't help but feel I won't be looking left or right for a few days."
On Saturday, Mallinder said: "Our doctors and medical staff are really clear that if anyone gets knocked unconscious or has had a knock where they look like they are unconscious, they need to come straight off.
"It's as simple as that. You don't go to be assessed - you are off straight away. George has had some previous issues so he took it steady.
"The doctor was very, very happy even as he walked off that he was just going to go for an assessment and thankfully he could come back on."
A club statement said that North was "communicating immediately with attending medics" and "complaining of neck pain".
It added: "Significant neck injury was excluded on the field but on review of video footage pitch side, the team followed World Rugby protocols and used a Head Injury Assessment given the potential mechanism for head injury.
"George was fully assessed by the doctor and passed fit to return to play."
But Northampton then released another statement on Tuesday, which said: "It is important to note this video footage is not always the full range of replay angles available to the TV viewing audience at home.
"If evidence suggesting a loss of consciousness had been available to the medical team at the time of assessment, George would not have been allowed to return to the field of play."
Chris Jones, BBC Radio 5 live rugby union reporter
This is turning into a very significant story, with Northampton saying that their medics did not have access to all of the television footage to review North's fall, so rather than withdraw him permanently from the field, they took him off for a head injury assessment, which he subsequently passed.
But if it is the case that the right footage was not available, then it makes a mockery of the system.
Medics have access to instant replays of collisions precisely to avoid a situation like this happening.
The independent review will look to establish whether the right footage was not available, or if it was, but Northampton did not use it appropriately. If it is the latter, Saints could face punishment.
North's history of head injuries, which included four head blows in five months between November 2014 and March 2015, including two in one game against England in the Six Nations, added additional concern.
He was left unconscious in a Premiership match against Wasps in March 2015, leading to a spell on the sidelines that lasted from 27 March to 29 August.
In the aftermath of the game, Premiership Rugby confirmed the incident will be reviewed as part of a normal procedure.
"Every head injury incident that occurs in Aviva Premiership Rugby is assessed by an independent reviewer as part of our procedure to manage concussion," said a spokesman on Saturday.
"This is a world-leading system of assessment to ensure we take a comprehensive look at every incident which involves a potential head injury.
"Player welfare is our number one priority so all incidents in our 135 matches are reviewed thoroughly."
Brain injury charity Headway have called for an investigation into why the medical staff did not have full access to TV replays.
Peter McCabe, chief executive of Headway, said: "This incident is extremely worrying as it involves a player who has had lengthy periods out of the game due to concussion.
"It's also a repeat of an incident which happened while George North was playing for Wales last year. In that game, full TV footage was not used in the assessment process for a head injury. It is time rugby authorities learned from previous mistakes."
Meanwhile, the club has not given a timescale on how long the independent review will take to complete.
Premiership Rugby and Rugby Football Union officials have held an urgent meeting to assess the handling of George North's latest head injury.