The man who owns them rigged a harness up for his cat so she wouldn't have to walk so much (like the dog and himself). At some point, the rat came along, and as no one wanted to eat anyone else, the rat started riding with the cat and, often, on the cat!
The dog will stand all day and let you talk to him and admire him for a few chin scratches. The Mayor of Santa Barbara filmed this clip and sent it out as a holiday card.
http://www.youtube.com/watch_popup?v=D85yrIgA4Nk&feature=player_embedded