Cops say Starr -- who appeared on "Celebrity Rehab" in 2009 -- was in possession of 6 pills of a painkiller called Opana and 6 pills of Xanax ... an anti-anxiety drug.
According to the documents, Starr didn't have a prescription for either drug -- and was arrested on 2 felony counts of possession of a controlled substance.
Starr was taken to a nearby police station ... where he is still being held on $20,000 bail.
UPDATE: According to the police report, Mike tried to pull the whole "Do you know who I am?" card -- saying"
"[Mike] stated 'Hey officer, have you heard of Alice in Chains? I used to be the base [sic] guitarist for them. We are down here in Utah. Me and Travis are putting together a new band.'"