Season 1: Episode 07: Brian: Portrait of a Dog
Peter enters Brian in a dog show for some extra money, and although Brian originally agrees to perform, once he realizes that he'll have to beg for a treat he decides it's all too humiliating. After not receiving the respect he feels he deserves at home, Brian takes off, returning to the streets where Peter originally found him, and gets arrested and sentenced to death. It's up to Peter to save him, and he does so by bribing the city council.