The Coroner's Office just released the certificate, filed in L.A. County ... and it lists cause of death as asphyxia by hanging. It also says he was found dead in a riverbed in Sunland, CA.

TMZ broke the story ... Salling was found hanging from a tree ... not far from where he lived. The Coroner had already determined it was death by suicide, as we reported.

We still do not have toxicology results from Salling's autopsy ... which will show if he had been drinking or boozing prior to hanging himself.

Prior to killing himself, the "Glee" star has pled guilty to possession of child pornography involving prepubescent minors and was awaiting sentencing.