I don't have the actual printed rules in front of me, but this is what I had downloaded from the last proofreading for the 2nd edition. Emphasis is mine:
The game ends immediately with a WIN for the Good Cops if any of the following conditions occur:
1. The Murder Suspect is arrested. Remember that, in order to make the Arrest, the District Attorney must feel there is enough evidence to win a trial (this means that ALL of the evidence MUST be collected on the Murder Investigation Board).
2. The Murder Suspect has not yet made his appearance on the board, AND all of the Evidence has been gathered. In this case, NO arrest is needed (an automatic win occurs!)
Immediately means you don't have to finish the turn...you win!