The court and surrounding area in Celle, northern Germany, have been evacuated.
Police understand a “legal dispute” led to the tragedies in the foyer of the building, moments before the case was to get underway.
But officers stressed there is no longer a danger to members of the public.
One police officer addressed media at the scene.
Her statement, roughly translated to English, said: “Two people are said to have already been injured when the emergency services arrived.
These two people – a man and a woman – died at the scene. Our initial findings suggest the whole thing happened in such a way that the man shot the woman and then shot himself.”
(dpa/NAN)