Michael Corleone makes a public announcements where he says: "He is deeply saddened by the events taken place at the hospital, I hope that whoever brought this misery upon my poor friend shall pay. I also want to tell the German mob that I have no quarrel with them and this act of violence was uncalled for and we shall take no revenge." This is received greatly by the press because of the influence that the Corleones have and the Germans are evn more under pressure. The police are now mainly focused on their activities in their territory.
Captain Barner has been given orders to search all establishments in his precinct which could potentially hold German gang hideouts. Groups of police officers will begin searching throughout the triangle.
Don't kill anyone. Just make it look like the Italians are at war. Spread it to both families, lower order will start to fight.