Six Nations Rugby gathered material from the Rugby Football Union (RFU) and the Scottish Rugby Union (SRU) plus the BBC and match officials and looked at video footage for their probe.
"There was some evidence of pushing and shoving in the tunnel at the relevant time but no clear evidence of violent conduct or similar against any individual player," Six Nations Rugby said in a statement on Wednesday.
"No further disciplinary action will be taken."
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It added that the RFU and SRU would be reminded about their players' obligation to uphold the reputation of the tournament.
England travel to France for their next clash on March 10 when Scotland visit Ireland.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Ken Ferris)
