Yet ANOTHER "GODFATHER" Question!

Sorry, I gfuess I’m a GF junkie! Anyway, I noticed this while watching it on AMC for the jillionth time: When michael, Sonny, and Tom Hagen are discussing whacking Solluzzo and the NYC Police Captain (who busted Michael’s nose), Tom Hagen says something like:
“Nobody’s ever killed a NYC police captain! The “Five Families” would be all over us…it can’t be done…”
Was there an unwritten law in the Mafia (against murdering policemen)? I know Dutch Schultz (the jewish bootlegger) was killed because he proposed whackinng NYC atty. general Thomas Dewy.
Was the Mafia afraid of public reaction (if they killed a policeman)? In Sicily.policemen (from the cop on the beat to a police general) seem to be fait game for the Mafia!

Pissing off the police would destroy the efficiency of the Mafia. It is better for them to not piss off the police to the point where the police will no longer just look the other way for some cash. Kill a cop and you possibly change the whole game. While the police probably can’t destroy the mafia, they can make it less effiecient and that will cost the Mafia money. Remember, this is a business.

You don’t whack coppers 'cuz the coppers will step up the heat, bringing the family’s operations to a halt.

Plus, in GD the NYC cops were “employees” of the Five Families, taking bribes to look the other way. The police captain Michael whacked was one of these.

The cops and the mob have a delicate symbiotic relationship set up. A police captain getting whacked will upset that, so the cops will start kicking some Mafioso ass. It would change the whole scene.

Others already nailed it, I’ll add a quote from Vito about the relationship:

"Even the police departments have helped us in the past with gambling and other things. They’re gonna refuse to help us when it comes to narcotics. And I believe that then - and I believe that now."

Petty stuff and gang-on-gang violence was OK, cop-killing and hard drugs broke the contract. Of course Michael found a way around this by using contacts in the press, he was one clever paisan.