Deputy Police Chief Doug Lepard said there was no indication of foul play. Monteith's body was found by hotel staff after he missed his check-out time, Lepard said.
"We do not have a great deal of information as to cause of death," Coroner Lisa Lapointe said.
Lepard said Monteith had been out with people earlier and that those people are being interviewed.
"We are deeply saddened by this tragic news," "Glee" and Fox said in a joint statement. "Cory was an exceptional talent and an even more exceptional person. He was a true joy to work with and we will all miss him tremendously. Our thoughts and prayers are with his family and loved ones."
Cory Monteith's Death Shocks 'Glee' Family
In April, he admitted himself to a treatment facility for "substance addiction" and asked for privacy as he took steps toward recovery, a representative said at the time.
Lea Michele, his "Glee" co-star and real-life girlfriend, told People magazine that she loved and supported Monteith and was proud he was seeking help.
It was not Monteith's first time in rehab. He received treatment when he was 19 and had previously talked about his addiction struggles, saying he had a serious problem and took just "anything and everything."
He told Parade in 2011 that he was "lucky to be alive."
Monteith, who turned 31 on May 11, starred in "Glee" as Finn Hudson, a high school football player who puts his status and popularity at risk to join the glee club and its outcast members.
With 'Glee,' Cory Monteith Made History On The Hot 100
Michele played his on-air girlfriend in "Glee," Rachel Berry.
The show, with its pop music-based musical numbers and high-profile guest stars including Gwyneth Paltrow, became an immediate hit and made stars of its relatively unknown cast.
On his Twitter account, Monteith described himself as "tall, awkward, canadian, actor, drummer, person."