A gunman opened fire at a building in Cincinnati, in the US state of Ohio, killing three persons and injuring five others, officials said on Thursday."Five victims injured, three dead. Suspect is dead. Three or four officers responded and engaged the shooter," the Cincinnati Police Department tweeted.The incident took place at a 30-storey building, home to the corporate headquarters for regional banker Fifth Third Bank and other businesses, Xinhua news agency reported.Police said the gunman opened fire at the loading dock of the building and then entered the bank's lobby where he exchanged gunfire with police.It's unclear if the gunman shot himself or was shot by officers.The gunman was not identified, and police did not comment on the possible motive.One of the victims died at the scene and two more died at the University of Cincinnati Medical Centre, according to reports.A spokeswoman for the medical facility said one victim remained there in critical condition and another was listed as serious. All four treated at the hospital suffered from gunshot wounds, she said.In a statement, Fifth Third Bank offered thoughts and prayers for those caught up in the "terrible event".The bank operates around 1,200 banking centres in 10 US states.