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11:43 AM PT -- Russillo drunkenly passed out in a stranger's bed ... cops say.

Long story short, cops were called to a home by the owner around 3:30 AM on Wednesday to report a strange man sleeping in one of the bedrooms.

When cops arrived, they found Russillo who appeared to be hammered out of his face -- "blood shot glassy eyes, very slurred speech and could not answer questions coherently, all signs of alcohol intoxication."

Cops say Russillo didn't know where he was or where he was supposed to be staying.

Officers also don't believe he forced entry -- and say he got in the house through a door that hadn't been secured properly.

He was charged with criminal trespass -- and could face a $750 fine.

ESPN host Ryen Russillo -- who's appeared on ESPN radio and TV since 2009 -- was arrested in Wyoming for criminal entry ... TMZ Sports has learned.

We know 42-year-old Russillo was taken into custody on Wednesday and is still locked up as of the time of this post, according to officials.

Details surrounding Russillo's arrest are unclear. We're working on it.

Russillo currently has his own show on ESPNews -- "The Ryen Russillo Show" -- but he's obviously not hosting today. Will Cain is filling in and announced he'll be doing so the rest of the week.

Ryen previously co-hosted the "SVP and Russillo" show on ESPN with Scott Van Pelt.