Two of the girls, who are 19 and 20 years old, had attended the show on Monday night before the attacks allegedly took place.
A fourth woman reported being put in a stranglehold by an unknown man during the event, Adressavisen newspaper reported.
"Two of these most likely happened in connection with the UKA event Life in Color," Rune Brandmo with the Trondheim Police told VG.
The show, billed by its organizers as the "world's largest paint party", was established by US house producers Sebastian Solano, Paul Campbell, Lukasz and Patryk Tracz.
It was brought to Trondheim as part of UKA, a popular music festival organised by students in the city.