Police say viewers need to exercise their own judgment in separating reports that are accurate from one's that aren't. Police earlier Sunday had said that Stephens had broadcast it on Facebook Live.
Police say he should be considered armed and unsafe.
Dr. McCoy said many times, online criminals are looking to hurt as many people as possible, as fast as they can.
Authorities say multiple 911 calls came in shortly after 12:30 p.m. Monday claiming that Stephens could be in or near Fairmount Park, a large green expanse northwest of downtown.
A handful of schools in the Fairmount Park area were placed on lockdown.
Authorities were assuming he was still with his vehicle more than 24 hours later, and discounted reports that he might be on the run in Pennsylvania.
Facebook disabled the suspect's account within 23 minutes of learning about the killing video, and "two hours after receiving a report of any kind".
He had worked since 2008 as a vocational specialist and youth mentor at Beech Brook, a behavioural health agency located outside Cleveland.
Stephens was discharged from bankruptcy in August 2015, federal court records show.
Stephens had referred to himself as a case manager.
"No, I'm not going to watch it", Debbie Godwin said.
The local and federal manhunt - which includes the FBI and U.S. Marshals - has expanded to five states: Pennsylvania, New York, Indiana and MI.
Chief Williams warned residents to be careful as the go about their day.
Mr Godwin, a father of nine and grandfather of 14, was shot walking home after enjoying an Easter meal with his children. "My heart and prayers goes out to the family members", she said in a text message statement to the network.
Williams stressed that investigators don't know where Stephens is and said his last known location was at the scene of the Cleveland slaying.
He could also be in New York, Indiana or Michigan, WLS-TV noted.
"If you see me again, it'll be a miracle", she quoted him as saying.
Cleveland police and USA marshals have requested additional backup to search for Stephens in New York, Michigan and Indiana.
Stephens reportedly made Godwin say the name "Joy Lane" before he pulled he trigger and killed the man in cold blood in broad daylight.
Users across the internet say they are frightened, concerned, and even disturbed by what they saw in Stephens' video. They planned to provide updates on the search at a news conference later Monday morning. The company envisioned live video as a tool to bring people closer together, but the dark, unexpected effect has been the raft of suicides, rapes and murders that have appeared on the site.
The victim, retired foundry worker Robert Godwin Sr., apparently was shot while out on a walk to collect discarded aluminum cans in a plastic shopping bag, something his son toldCleveland.com that Godwin did often.
The FBI is helping with the investigation.
"I'm about to keep killing until they catch me", the suspect said on one of the Facebook videos.
But what happens when the wrong information is passed along, such as Sunday's murder posted to Facebook in Cleveland?
"We forgive him, we forgive him", one of Godwin's daughters about Stephens.
In the video, Stephens names a woman and tells the victim, Robert Godwin, that "she's the reason that this is about to happen to you".
A reward of $50,000 was being offered for information regarding Stephens's location, officials said.