People who grew up in the south often use a variety of expressions to describe intoxication or drug-induced befuddlement. One of them is "Drunk(High) as Cooter Brown" or "Drunk(High) as Cooty Brown":
Drunk as Cooter Brown; drunker than Cooter Brown -- Very drunk indeed. Who the proverbial Cooter Brown is no one seems to know, but this may have originally been a black expression from the Carolinas. 'In Texas we'd call him drunker than Cooter Brown.'Whistlin' Dixie: A Dictionary of Southern Expressions by Robert Hendrickson
DRUNK AS COOTER BROWN - adj. phrase. Also "drunk as Cooter, ~ Cooty Brown. Chiefly South. Very intoxicated. "This is a Black expression very familiar to the informant, who is from New Jersey. She says it is current and, so far as she knows, it 'came up with the Blacks from the Carolinas.' She thinks it probably derives from some proverbial drunkard."Dictionary of American Regional English, Volume 1 by Frederic G. Cassidy
A peculiar expression, indeed. Wherever could it have originated? One confabulated explanation has it that during the Civil War, a man named Cooter Brown had family on both sides. Not wanted to fight for either North or South he stayed drunk for the entire war. This is, of course, ludicrous as he would have been drafted by the first side to find him and thrown in the brig for a few days to sober up.
A more likely derivation is from "cooter," the slang term for a turtle. Another spelling is "coota." The derivation seems to be the West African words "kuta," "nkuda," or "kuts," all meaning a turtle. (I wrote up a similar influence of West African language on southern slang in my entry on the origins of the phrase shotgun shack.)
Now, what does it mean to be as drunk as a turtle? Slow, lumbering, unable to perform any complicated task. It may not make a lot of sense, but it's the best explanation I've seen.