On this page of the Disco Elysium game guide, you will find a detailed walkthrough of The pissing competition task.
In Disco Elysium, during the task The pissing competiton, you will have a discussion with Kim about the unusual competition between precinct 41 and precinct 57. This task unlocks automatically once you have inspected the hanged man's corpse.
During the conversation with Kim, ask him about the pissing competition and exhaust all the available dialog options, then wrap up this side story by selecting Okay, enough of the competition then. Tell me something else.