Isaac said Perez died after the first officers on the scene shot him multiple times.
Bank employees sheltered in situ for an hour or more as officers swept the building and cordoned off several downtown city blocks.
The chief says they had a "quick response" and 'there is no additional threat'.
The incident occurred after 9:00 am local time (1300 GMT) at the lobby and loading dock of the 30-story Fifth Third Bank building in the city's downtown business district. This is abnormal. No other industrialised country has this level of active multiple shooting on a regular basis...
The situation appeared to be under control shortly before 7 a.m.
After the incident was over, police said four people, including the gunman, were dead. A phalanx of police officers and ambulances rushed to the scene at the height of morning rush.
Michael Richardson, who works in the building, was just outside the main doors smoking a cigarette when he heard gunshots. He did not work at Fifth Third or any nearby businesses, according to police. Although people tried to get her attention before she entered the building, she was wearing headphones and did not hear them.
One victim was at a Graeter's ice cream shop in the area while another was 5th and Walnut streets, the Enquirer reported. "We're a bit rattled".
Londberg quoted the witness as saying, "I saw a guy in a white shirt walking around and shooting like this" (the witness held up his right arm straight in front of him) 'bing bing bing bing, '" and then added, "He ran.
Radio traffic indicated other victims may have been transported to Good Samaritan Hospital. "Witness to Cincinnati active shooting: Witness was sitting in Fountain Square when teens outside Fifth Third Bank yelled that there was a shooter. We didn't know where to go because we didn't have a backdoor", she told reporters. Leonard Cain tells The Cincinnati Enquirer that he was about to walk into the bank until someone told him about the shooting.
Perez's aunt said her nephew held various jobs and was now working, though his aunt and her family did not know where.
Fifth Third, which operates 1,200 banking centers across several states, in a statement offered its "thoughts and prayers" for everyone "caught up in this bad event".