Don Corleone is worried about disloyalty among his chiefs and judges. Find the police official at the party, and pay him off as a reminder of the Corleones' allegiance to its men. The official is a smoker and good with women.
Reward: +2,500 Respect
Go to the basement of Harry's Bar where the police party is taking place. The cop you're looking for should be the farthest one to the left. You'll know you have the right one because he'll be the only one who is both smoking and talking to a woman. Talk to him. He'll tell you he's busy. Now talk to the woman next to him and tell her to get lost. Now you're free to talk business, so talk to the cop again and bribe him. He'll accept the bribe and also let you know that Fredo Corleone is in some sort of trouble with the police. This sets up the next favor.