A spokesman for the Cuyahoga County Sheriff's Department also said that Griffin had broken free.
Elliott said that his agency first learned of Elliott's escape after being contacted by the sheriff's office to assist with the case.
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An escape warrant has been issued and the U.S. Marshal said Griffin should be considered armed and dangerous.
"We hope to have a peaceful resolution to this at end of the day. We're out there right now and were looking," Elliott said.
In January, Griffin was arrested and charged with rape, felonious assault and kidnapping in connection with a domestic violence attack on his 42-year-old girlfriend at their Parma, Ohio, home.
Police say Griffin pistol-whipped his girlfriend and fired two shots near to her during the attack.
After that arrest, more than 60 firearms were found in his home, including 50 handguns, five assault rifles, seven long rifles, four shotguns, and an Uzi submachine gun, according to NBC affiliate WKYC.