The club last week fined the former Hibernian striker after footage showed him singing "Hearts are going bust" in a public house before attending the Leith side's 2-0 defeat at Tynecastle.
However, Police Scotland has said it is investigating an incident over the singing of a derogatory song about former Hearts player Rudi Skacel.
Celtic said in a statement last night: "Due to an ongoing police investigation we are unable to comment. However, the club takes the allegations extremely seriously and have launched our own internal investigation."
Griffiths faces Scottish Football Association disciplinary action over the "Hearts are going bust" footage.
Vincent Lunny, the SFA compliance officer, has also been studying the fresh footage. He could issue a second notice of complaint to the Scotland striker but, more likely, the charge will be re-issued taking into account the new footage.
Neil Lennon, the Celtic manager, last week warned Griffiths, who joined the SPFL Premiership champions from Wolverhampton Wanderers in January, that the transgression was "his one strike". He has also previously stated his "zero tolerance" approach to racist incidents.
Griffiths is believed to have been fined the maximum four weeks' wages for his singing in the Roseburn Bar and unequivocally told that such conduct would not be tolerated.
The club captain, Scott Brown, would not speak specifically about Griffiths at a news conference yesterday to announce season-ticket pricing for next season. However, he followed a similar route from Hibs to Celtic and said of the change in culture: "Expectation on you is ridiculous and everyone thinks they know you. People come up and say: 'Broony how you doing?'
"You never got that at Hibs. You got a few folk coming up and slapping you on the head. Celtic is a great place to be but it's not easy. The new lads have been brilliant in training and away from the park, though."
Asked if it was difficult to relax in the city, he said: "I haven't been in Glasgow since I signed for Celtic."