I was restarting the game the other day and I rushed through everything, and I managed to kill Officer Gomez with the BB Gun. Here's how I pretty much did it: You have to rush the dialogues. When you talk to Butch, insult his Mother's drinking habits to make him attack you. You will need to talk to Gomez right after the conversation with Butch ends, right before Gomez starts to get up from his chair. Tell him that Butch tried to take your sweetroll so he confronts Butch. If you did it right, he will start chasing you to ask if you are fine AFTER he talks to Butch. Try to prevent him from talking to you at all until you are in the shooting range and have your BB Gun. If you do it right, he will chase you into the shooting range, and he will be locked in the area just like you are. Now you will be able to kill him using the BB Gun. When attacked, he will freak out and won't fight back. Your dad and Jonas will ignore that you are killing him and you won't get negative karma either, but you do receive 10 points of experience. You can wear his clothes and can use his baton normally. (Done on the 360 version)
Has anyone else been able to do this? I haven't been able to recreate it, sadly. I almost did it once, by running from Gomez while locked inside the party's room. Daddy took too much time talking to Jonas so Gomez got me before I was in the shooting range.
Hope it's easy to understand what I'm saying.