The SPL will ask Motherwell and Hearts to respond to claims of racist chanting and sectarian singing.
Laryea Kingston scored one and set up the other against Well
The report from Monday's match delegate is understood to mention possible abuse aimed at Hearts' Laryea Kingston.
Observer Allan Preston is also thought to have been aware of alleged sectarian content in some Hearts fans' songs.
No official complaint was made on the night of the match, but the police and match officials will also be asked for their feedback to the report.
Motherwell issued an apology in March after St Johnstone striker Jason Scotland was abused during a Scottish Cup tie at Fir Park.
But the Fir Park club were quick to play down claims of racism from their fans this time.
"It appears a match official mentioned to a police officer that he may have heard something untoward but could not be sure," said a club spokesman.
"The police looked into it and have confirmed they are not investigating and Hearts are making no complaint.
"We would like to make it absolutely clear that this club does not tolerate any form of bigotry or racism."
The SPL have created a new offence of unacceptable conduct at their matches which covers violence and disorder generally and sectarian conduct in particular.
These regulations were developed with reference to Fifa and Uefa regulations, discrimination law - racial and religious - and football banning orders.
After the 2-0 win for the visitors, Hearts assistant coach Stephen Frail said: "I never heard any racial abuse from anyone.
"We would like to stamp that out but from where I was standing I have not heard anything."