The 31-year-old was found dead in his hotel room at the Fairmont Pacific Rim hotel in downtown Vancouver, British Columbia, Saturday. No foul play was suspected.
Monteith had checked into the hotel on July 6 and was supposed to check out on Saturday. When he didn't, hotel staff checked his room and found him dead, the BC Coroners Service said in a statement.
"The investigation into this death by the BC Coroners Service is continuing, and no other details are available at this time," the statement said. "It should be noted that at this point there is no evidence to suggest Mr. Monteith's death was anything other than a most-tragic accident."
The publicist for Monteith's girlfriend and "Glee" co-star, Lea Michele, said in a statement, "Since Cory's passing, Lea has been grieving alongside his family and making appropriate arrangements with them. They are supporting each other as they endure this profound loss together."
Monteith spoke openly many times about his substance abuse problems. In 2011, he told Parade magazine that he was "lucky to be alive." He checked himself into rehab in April. It was not Monteith's first time in rehab. He also received treatment when he was 19.
The Associated Press contributed to this report.