(CNN) -- Four police officers were shot at a Detroit police precinct on Sunday afternoon but all are expected to survive, the city's police chief said Sunday. Security measures may be reassessed now, he said.
The most seriously injured officer -- he was shot in the lower back -- emerged from surgery Sunday evening at Sinai-Grace Hospital, Detroit Police Chief Ralph Godbee said.
A person who police identified as the shooter was shot dead, Godbee said at a Sunday evening press conference.
Police have identified the shooter, Godbee said, but are withholding the person's name as they conduct an investigation of the incident.
Godbee said that a man walked into a police precinct Sunday and "indiscriminately began firing and as you can imagine utter chaos and pandemonium took place."
"Through it all, our officers maintained courageous calm," he said. "They returned fire, they took cover, they did all the things we train them to do under pressure."
Godbee said the "prognosis we feel is very good" for the officer who was shot in the back, who is a commander.
A female sergeant was shot in the chest but was protected by a bulletproof vest. She has been treated and released from the hospital, Godbee said.
Two other male officers were grazed in the head, with one in serious condition, but both are conscious, alert and talking, he said
"We are very relieved that it appears that all our officers are going to be OK," Godbee said.
He said the identities of the wounded officers are being withheld until their families are notified.
Detroit Police Department Sgt. Eren Stephens said the shooter was a 35-year-old African-American man. He walked into Detroit's sixth precinct station Sunday at 4:25 p.m., and "opened fire, striking 4 officers," Stephens said. "Return fire fatally wounded the assailant."
Godbee said Sunday that Detroit police would likely revise security measures after the shooting. He referred to the Tucson, Arizona shooting that left six dead and wounded 13, including U.S. Rep. Gabrielle Giffords, earlier this month.
"In light of what happened in Tucson, Arizona, with Congresswoman Giffords and then with this incident, of course we have to take a step back and reassess security procedures at each one of our facilities," he said.
"It's more than likely we will be changing a number of things relative to standard operating procedures as to how we screen our public before they come in," he continued. "We want to still maintain community policing format, we want to engage our public but at the same time incidents like this are very sobering (and) remind us how vulnerable we all are, especially in the public sector."