Eugene works for Pawnee Animal Control along with Brett and Harris. Leslie describes them as "burnt-out morons". Pawnee: The Greatest Town in America states that Harris and Brett took over as Co-Directors after Eugene retired last year, presumably to spend more time with his bong.
In "The Possum", Leslie Knope is asked to assemble a task force to catch Fairway Frank, a possum accused of biting Mayor Gunderson's dog. When she asks for the two best guys to join her and be part of her task force, Eugene tells her that would be Brett and Harris. At first, he tries to tell her that they're not there, even though they're standing right behind him. Tom Haverford calls out Brett's name, and he answers.