Police earlier had said that Stephens had broadcast it on Facebook Live.
Stephens uploaded a video to his Facebook page showing a gun pointed at an unidentified man's head. At a police press conference, Cleveland Police Chief Calvin D. Williams said that "the last location we actually had [Stephens] at was the homicide".
In the video, Stephens said he snapped because of a woman, and then later claimed to have killed more than a dozen other people.
Although Stephens claimed responsibility for additional killings, authorities have only confirmed one victim.
Police say Steve Stephens shot Goodwin on Sunday afternoon while he was recording live on Facebook. Authorities have warned people in Pennsylvania, New York, Indiana and MI to be alert for him, and the FBI is assisting in the investigation.
Police believe Stephens might have left the state of Ohio.
An Ohio man who allegedly fatally shot a senior citizen and shared the footage on Facebook may be in Pennsylvania, New York, Indiana or MI.
"Yeah", Stephens replied. "She's the reason why this is about to happen to you".
Police identify the suspect as Steve Stephens.More news: Milan snatch extraordinary draw with Inter in first Chinese derby
"Any problems he is having, we can have a conversation".
They had no comment on the search in Philadelphia, other than to say every lead is being followed to find Stephens. In his last video, Stephen said he "snapped" and will continue killing until he is caught.
Stephens began filming one of the videos while sitting in his auto.
Stephens worked at Beech Brook, a behavioral health agency headquartered in Pepper Pike, near Cleveland.
Stephens is black, just over 6-feet tall and bald with a full beard.
"Got my nephew. Today's his 5th birthday, teaching him how to fish", Stephens says to the boy, who is seen standing on a bridge with a fishing pole.
The 37-year-old suspect is considered armed and unsafe and claims he has killed more people, but police have not verified any more homicides.
"I woke up Friday and I just couldn't take it anymore", one post reads, before going on to make a number of threats saying he is going to shoot people and wants to end up on death row. Police said he might be driving a white or cream-colored Ford Fusion, and asked anyone who spots him or his vehicle to call police or a special Federal Bureau of Investigation hotline (800-CALLFBI).
Mr Williams said that "multiple forces" were looking for Mr Stephens, who "needs to turn himself in".