"The figure of Yatsufusa is from the epic novel Nansō Satomi Hakkenden by Kyokutei Bakin. In the novel, Lord Satomi jokingly promises his daughter Fusehime's hand in marriage to a dog, Yatsufusa, if the animal can defeat his enemy, Lord Anzai. To his surprise, Yatsufusa returns with Lord Anzai's head. Lord Satomi does not wish to fulfill his promise to Yatsufusa, but Fusehime leaves with the dog anyway."
Short version: It's a persona in Persona 4. Also, it's story is referred in the game Okami. Both great games.
Battle hardened, quiet and though, not the kind of a personality you want to mess with. However, behind that hard cover, one can find a kind heart. At the end of the day he is the type that you can always rely on in times of trouble. All my other pets look up to him with silent respect.
As a police officer he has seen it and heard it all. From his transformations you can see, that he has also been a prison pet. That was actually an undercover job he had to do once. His zombie look now is also a part of some current job, but he can't discuss the details.
All in all, it's clear that he takes his work rather seriously. Since his responsibilities also extend into battling, he is undergoing constant training, in order to keep fit. He is the ultimate guardian of justice. He leaves Serafi alone on purpose though. He knows Serafi is harmless.