The Harajuku Zoo first appeared in Music Zoo. It is managed by Mr. Smythe and there are no other known workers besides him. There are various exhibits set up and it's home of the Harajuku Zoo Acrobats, a group of dedicated performers who do various stunts and acts.
Music would cause a lot trouble at the zoo as a child, which caused her to fail a background check, effectively banning her from the zoo. She was able to get a probation period, which she passed. However, Baby also failed a background check effectively banning her as well.
There is an official zoo rulebook.