See Post #71 for Step 2 in the process.
Why keep it secret? It would be outstanding PR that they caught the guy. Otherwise, it just goes away and is chalked up to one more instance of police stupidity.
Balance that against, I assume a greater punishment for the perp if done in secret? That doesn't seem reasonable. Can they get more info from the perp if the whole thing is kept secret? THAT could be a prime concideration.