The authorities in Ohio said Wednesday that they had begun two separate investigations into the death of Ariel Castro, the Cleveland man sentenced to life in prison for holding three women captive in his home for a decade.

Mr. Castro, 53, hanged himself with a sheet on Tuesday night in his cell at the Correctional Reception Center in Orient, near Columbus, officials said. He was being held there temporarily after a Cuyahoga County judge sentenced him to life in prison last month.

Jan M. Gorniak, the coroner of Franklin County, said that an autopsy had determined that Mr. Castro’s death was a suicide. The determination prompted Mr. Castro’s lawyers to call for an investigation related to the level of care and supervision provided to him, saying that he had a history of grave psychological problems, including suicidal thoughts, before being transferred to the state facility from a county jail in Cleveland.

“Mr. Castro’s psychological history reflected depression and suicidal tendencies, which is why the county jail placed him on suicide watch,” said Craig T. Weintraub, one of Mr. Castro’s lawyers. “Typically, any time someone is sentenced to prison there is profound depression, especially if it is a life sentence without the possibility of parole.” Late Wednesday, Ohio prisons officials said they had begun a review of Mr. Castro’s death. A separate investigation will be conducted by the Ohio State Highway Patrol.