The fair reopened on Monday following a memorial service to honor those who died.
Fair spokesman Andy Klotz said initially that the state fire marshal's office was responsible for inspections, but he backtracked Monday, saying he wasn't sure whose job it is.
Investigators are trying to determine whether anything could have been done to prevent the collapse.
The accident happened when a wind gust estimated at 60 to 70 miles per hour toppled the roof and the metal scaffolding holding lights and other equipment.
The stage collapsed onto a crowd of concert-goers awaiting a show by the country group Sugarland.
Another emerging issue is whether fair organizers responded quickly enough to forecasts of an approaching storm, especially since a different concert nearby was canceled because of the weather.
Organizers of the Indianapolis Symphony Orchestra got the same forecast and decided to evacuated the 6,700 people from the Conner Prairie Amphitheater.
"We saw a storm that contained lightning dip south a little bit. Once we saw that, I made the decision to stop the concert and send everyone to their cars," said Tom Ramsey, the orchestra's vice president and general manager.
At the fairgrounds, concert-goers and other witnesses said an announcer warned them of bad weather, but there were no warnings to clear the area.
Klotz said fair executive director Cindy Hoye and Indiana State Police Capt. Brad Weaver made the decision to evacuate the grandstand within two or three minutes of the bad weather announcement and that they were headed to the stage to order an evacuation when it collapsed.
"The decision was made to make it a mandatory evacuation and we never got to the microphone," Klotz said.
The Associated Press contributed to this report.