Authorities say Michael Madison, 35, may have been influenced by convicted serial killer Anthony Sowell, also known as the Cleveland Strangler.
Madison did not enter a plea when he appeared in court, where his bail was set at $6 million. He waived his right to a preliminary hearing.
Only one of the victims, Angela Deskins, has been identified. She was believed to be 38 years old. The other two bodies were too badly decomposed to identify. The medical examiner also said he couldn't determine a cause of death because of the bodies' conditions.
The first body was found in a garage Friday. Two others were found Saturday - one in a backyard and the other in the basement of a vacant house. The bodies were found about 150 yards apart, and investigators believe the victims were killed in the previous six to 10 days.
ABC News and the Associated Press contributed to this report.