Carter, 24, is charged with murder and attempted robbery in the July 18, 2010 death of Officer Bailey.
Bailey was washing his car outside his Chatham home on the city's South Side when he was shot to death. He had just gotten off a security detail for former Richard M. Daley.
Investigator say Carter -- who is jailed on a separate, unrelated case of carjacking -- bragged about Bailey's murder, which led to a break in the case. They say he wrote letters from his prison cell and spoke with other inmates about Bailey's murder.
Carter has an extensive criminal history that includes the aggravated battery of a police officer. He was on parole in that case when he allegedly shot and killed Officer Bailey. Carter had been out of jail for only two months, officials say.
Police began questioning Carter about three weeks ago at a state prison where he was being held on a $50,000 bond related to the carjacking.