( CNN ) -- Five people died late Sunday in shootings at an apartment complex near Seattle , including the gunman who was shot by police , authorities said . A domestic dispute set off the events , said Brian Wilson , chief of police in Federal Way , Washington . A man got into a fight with a woman with whom he shared an apartment in the Pinewood apartment complex and fatally shot her , he said . The man then went to the parking lot of the apartment complex and fatally shot two men . The relationship between the gunman and the two victims in the lot is unclear , Wilson said . Wilson did not identify the gunman ; it was not clear why the identity was withheld . The gunman then returned to his apartment and retrieved a shotgun , he said . Neighbors who had heard the gunfire came into the hallway , and the gunman shot and killed one of those neighbors through an apartment door , Wilson said . Police intercepted the man on his way back to the parking lot , the police chief said . Police ordered the man to drop his weapon , but he refused , so the officers shot him , Wilson said . The man then dropped his weapon , continued to the parking lot and obtained another weapon . Police again ordered him to drop his weapon , he again refused , and police shot and killed him . Eight officers are on administrative leave , as is standard after officers fire at a suspect , Wilson said . The suspect had a valid concealed weapons permit , he said . When officers arrived at the scene in the city just south of Seattle , they could still hear gunfire , said police spokeswoman Cathy Schrock . They also saw two men lying wounded in a parking lot . No officers were injured . CNN 's Deanna Hackney contributed to this report .
NEW : Shooting in Federal Way , Washington , began with domestic dispute , police say . NEW : Gunman killed four people before being fatally shot by police . NEW : Ties between gunman , three of the victims are unclear , police chief says . Shots were still being fired when officers arrived , police spokeswoman says .