Police say they are aware of a video circulating online that appears to show a York City player punching a fan during celebrations after the club's dramatic 1-1 draw with Rochdale on Saturday.
York were promoted back to the Football League after a 10-year absence thanks to Josh Stones' equaliser in the 13th minute of stoppage time.
The club's triumph was followed by a pitch invasion, with footage appearing to show a fan putting his hands on a York player who was celebrating the moment on his knees with his head against the ground.
After an intervention by two stewards, the player stood up and broke free before appearing to punch the fan in the face.
"We are aware of a video that is circulating of a possible assault involving a player and we have linked in with both clubs and the National League," Greater Manchester Police said in a statement.
"We will be further assessing the video and reviewing CCTV of the incident."
The pitch invasion was the second of the match following one when Rochdale, who needed a victory to top the table and gain automatic promotion themselves, went ahead in the 96th minute.
Police said four Rochdale fans were arrested following the incidents, with one on suspicion of assault and pitch incursion, one on suspicion of a public order offence and two on suspicion of pitch incursion.
One male York City fan was arrested on suspicion of assault, with police saying he would be interviewed at a later date.
The incidents are also under investigation by the Football Association.
BBC Sport has approached York and Rochdale for comment.
York and Rochdale had amassed 212 points between them heading into the final-day showdown, with York needing to avoid defeat to secure a return to League Two.
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