Detective Joe Bourquin and Detective Steven Fine are the policemen who investigate Edward Blake's murder, but decide to let it "drop out of sight" out of fear that they'll have to deal with Rorschach's intervention. Joe says that he feels a chill right at the moment they pass by Walter Kovacs.
They also investigate the case of the murder of Clare and Dominique Hirsch by their father. While Bourquin says that the reason that many bad things have occurred are astrological and that most of those kinds of murders are media inspired, Fine implies that "The media inspires boredom, not waking up on a Monday morning and butchering your kids...". Joe tries to ease him into not letting the case ruin the rest of his day.
That evening, Joe was busy with the paperwork concerning Blake's file complaining that Fine had left it to him, that he didn't answer the phone and that he was tampering with evidence from the Hirsch house. The phone was an anonymous hint about capturing Rorschach. They were outside Edgar Jacobi's house with a police force, and Joe heard screams from the policemen, before Rorschach was forced to jump outside.
Joe also helps Steve to try and capture Daniel Dreiberg, but he escapes and Steve is suspended. Joe is with him in a type of police cab/car (that might be taking them home) and they both eventually die by the psychic wave.
While Steve seems to have a more rebel attitude towards the cases and his job (you could say the bad cop or the "cool" cop) Joe seems to be more like the worried boss, trying to get the job well done.
Joe also mentions that he has astrological beliefs, as noted in the case of Mrs. Hirsch.
In the Movie, Joe and Steve have minor appearance. Zack Snyder explained that they might be dealing with something bigger than them both.