Cuyahoga (ky-uh-HOH'-guh) County Jail officers Nicholas Evans and Timothy Dugan were accused of leaving the man in the restraint chair after the March incident and failing to get him proper medical care.
They initially were indicted on charges including felonious assault and unlawful restraint.
Evans on Tuesday pleaded guilty to attempted felonious assault and tampering with evidence. Dugan pleaded guilty to attempted abduction and misdemeanor assault.
Cleveland.com reports Dugan also agreed to cooperate with investigators in several cases that are on-going or still under investigation.
The officers' attorneys declined to comment after the hearing.
Sentencing is scheduled Dec. 12.
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