The investigation is continuing, according to the release, but it went on to say the 31-year-old actor's death appears to be accidental.
"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 service, which performed the autopsy and toxicology test on Monday, noted in a statement.
Monteith was found dead in his room at a Vancouver, Canada, hotel shortly after noon Saturday. When he hadn't checked out that morning, as expected, hotel staff checked on him and found the body.
The actor, who had long battled addiction, had recently completed a stint in rehab. His stay caused him to sit out the final episodes of "Glee's" fourth season as Finn Hudson. Still, his character's story was expected to pick up in the fifth season, which was set to begin production in a few weeks. How his death will be dealt with on the show has not yet been determined.