In the earlier games and New Leaf, Booker is a police officer at the Police Station. He is considerably less confident about his skills at this job than his partner, Copper. He runs the lost and found inside of the station.
Booker is instead a guard at the Gate in Wild World and City Folk, though he continues to run the lost and found. He is still stedfast partners with Copper.
New Leaf marks the first time he does not appear alongside Copper as only one of them can appear depending on which police station the player chooses to build as a Public Works Project.
In all games, Booker appears nervous and unsure of himself when talking to the player, hesitating to speak using words like "Um...", contrasting his partner Copper's confidence and bravery. He tells the player that this is because English is not his first language and he feels he isn't very good at it before quickly apologizing and clamming up.
In Animal Crossing and Animal Forest e+
In Animal Crossing and Animal Forest e+, Booker is a police officer running the lost and found inside the Police Station. He gives away any of the lost and found items, without questioning the player on whether they lost that item or not. He appears to question this to himself, by saying "Umm, okay, that's a lot of items," but never acts upon it.
In Wild World
In Wild World, Booker stands on the left of the gate inside the Town Gate. He will show the player the lost and found, tell them if visitors are in town (except Pascal, Pete and Gulliver) and change the flag to a different design. Like in the original Animal Crossing, he will give away any of the lost and found items away, without questioning the player.
In City Folk
Aside from slightly different speech, Booker's role in City Folk is exactly the same as in Wild World. He can be found in the same area, inside the town gate on the left hand side. Booker is very shy and unsure of letting the player change things (like the town flag) and letting them look inside the lost and found. He is also unsure of the exact time that people come through the town gate.
Booker enjoys going out of patrol, and describes that walking around outdoors hardly feels like work. This is likely an acknowledgment to the fact that he is a dog, and stereotypically, dogs enjoy going on walks.
When invited to the Campground via his amiibo Card, Booker may share with the player that he modified his RV himself, indicating that Booker is somewhat handy.