PITTSBURGH — A gunman who shot to death a worker and wounded six others at psychiatric hospital at the University of Pittsburgh this week was himself killed by campus police who had trained for a Virginia Tech-style shooting, authorities said.

John Shick began shooting almost immediately upon entering the lobby of the Western Psychiatric Institute and Clinic on Thursday afternoon, Pittsburgh major crimes Cmdr. Thomas Stangrecki said at a news conference Friday. Then, Shick went up a stairwell to a second-floor parking area, where he apparently tried to leave but couldn’t open a secured door. A window on the door was shot but didn’t shatter, suggesting Shick tried to shoot his way through.

Shick came back down the stairs and into the lobby, perhaps planning to escape through the front door. That’s where he encountered university police officers, firing at them through the door as they arrived.

Six Pitt officers had responded to the clinic within two minutes of the first emergency call, Pitt campus police Chief Tim Delaney said. They were trained to split into two groups of three to outflank the gunman and draw his attention.

The first three officers returned fire and killed Shick. So many shots were fired in the brief gunbattle that smoke hung in the lobby afterward, Delaney said.