"It is not clear whether the man shot himself or died because of the bullet wound inflicted by one of the police officers," police spokesman Ralf Meyer told reporters.
Meyer said the police were called to an apartment to intervene in a domestic dispute. A woman ran out of the door, followed by a man who shot her and both policemen. One of the officers returned fire.
The man holed up on a staircase, from where two more shots rang out. He died on the scene, Meyer said. The woman was wounded in the shoulder and stomach while the police sustained light injuries.