"There is no additional information at this time", the Wayne County office added.
The friend apparently forced open the hotel room's door and found the singer unconscious. Two Detroit newspapers had earlier cited a police spokesman Cornell was found with "a band around his neck".
He was best known for being one of the creators of the grunge movement.
Chris Cornell performs with Soundgarden at the 2011 Voodoo Experience.
Even without the benefit of hindsight from the morning's very bad news, it was clear that something wasn't right with the 52-year-old Cornell during the Fox performance.
Soundgarden bagged Grammys in 1995 for their songs Black Hole Sun and Spoonman.
RIP Chris Cornell, and thank you.
Cornell released five solo records and toured Australia in 2015 with a string of shows off the back of the album, Higher Truth. After splitting in 1997, they reunited in 2010 for their sixth studio album King Animal, with the band having sold more than 10.5 million records in the U.S. as of 2012 and winning two Grammy awards. He later went on to form Audioslave with members of Rage Against the Machine.
The Washington Post reported that "the banshee-voiced singer in the seminal Seattle band Soundgarden killed himself in a hotel room after playing a Wednesday night concert with the group, authorities said".
In addition to his music, Cornell also became involved in philanthropy and started the Chris and Vicky Cornell Foundation to support children facing challenges, including homelessness, poverty, abuse and neglect.