The Unalaska Department of Public Safety (Unalaska is a city in Alaska, weird ...we know) tells TMZ ... police responded to the famous "Cornelia Marie" on November 5, 2010 after receiving a call from Captain Derek Ray.
We're told Ray -- who took over the boat after the death of Captain Phil Harris -- told cops Phil's son Jake Harris (a deckhand on the boat) had been abusing prescription drugs while at sea.
Officials tell us ... cops searched the boat and found "paraphernalia" -- but not enough evidence to connect Jake to a crime.
Cops interviewed everyone on the boat -- but so far, no arrests have been made.
UPDATE: A rep for Jake told us "The facts of the case speak for itself, the Unalaska Department of Public Health has confirmed that no charges will be filed as a result of the investigation. Jake is looking forward to returning as part of the Cornelia Marie crew to the Bering Sea for the opilio crab season in January. "