First it will be hard to dispute the officers account that the pit bull ran at him/her. Assuming that you actually won a case in small claims court you might be able to get the $$ for the dog as well as some pain and suffering but this is doubtful based on the newspaper article that the dog charged the officer.

It might have been different if it was a different breed such as a Yorkie. It would be difficult for the officer to justify shooting a Yorkie when the Yorkie charged....but pit bulls kill people (also very loving) but they have the jaw strength to cause injury to a grown man.