On a farm, Daffy waits for his new Dick Tracy comic book to the tune of Raymond Scott's song Powerhouse. The mailman then arrives and he gets the comic book. To the tune of the Poet and Peasant overture, he sprints to a corner of the farm and reads it. Then, he wishes to become Dick Tracy and then knocks himself out by accidentally punching himself.
He then imagines himself to be "Duck Twacy, the famous detec-a-tive." Ignoring a piggy bank theft crime wave, he goes into action when he learns that his own bank has also been stolen from his secure safe. He calls a taxi to follow a car but leaves without him ("Keeps them on their toes."). Daffy, at one point bumped into one Sherlock Holmes and told him he is working on the side of the street.
Daffy's search leads him to a tram with Porky as the driver leading to the gangsters' not-so-secret hideout, where he faces off against all the dangerous criminals in town: Mouse Man, Snake Eyes (spoof of B.B. Eyes), 88 Teeth (spoof of 88 Keys), Hammerhead, Pussycat Puss (who looks like Sylvester), Bat Man (a name parody of the real Batman where DC Comics is now owned by WB), Doubleheader (spoof of Tulza "Haf-and-Haf" Tuzon), Pickle Puss (spoof of Pruneface), Pumpkinhead, Neon Noodle (spoof of Frankenstein), Jukebox Jaw, Wolfman (spoof of the real Wolf Man), Rubberhead, and a host of unnamed grotesques (the villains are obvious parodies of Dick Tracy's rogues gallery). He declares "You're all under arrest!!" The villans then roar at our hero and the chase begins.
In one sequence, the bad guys are seen using well-known Dick Tracy villain Flattop's head (perhaps a Mount Rushmore-style variant) as an airstrip with planes taking off. Rubberhead "rubs him out" with his head as an eraser but Daffy appears at the door. Pumpkinhead meanwhile moves in with submachine gun blazing. Daffy tosses a hand grenade directly to Pumpkinhead's head and he becomes a stack of pumpkin pies.
After being chased about, Daffy eventually turns the tables on the villains and traps them inside a hallway closet. He slams the door shut on them and eradicates the group with sustained fire from a Tommy gun (which, if this were not a cartoon, would be a grim scene indeed, echoing the climactic scene from Warner's film The Big Sleep, released the same year).
He faces one last adversary, Neon Noodle (who survived because he is a mere neon outline with no physical "center" for Daffy to shoot), whom Daffy defeats by turning into a neon sign that reads "Eat at Joe's" (a standard WB cartoon gag). He then finds the missing piggy banks, including his own. He begins to kiss his bank, but since he is dreaming he doesn't realize that he is on the farm again, kissing a real female pig. The plump yet slightly curvacious pig is rather smitten by Daffy since she believes he's trying to woo her with the barrage of smooches he plants all around her face while saying things like "I've found you at last!" He wraps his kisses up with a peck to the cute pig's little nose. So in an elegant female voice she says "Shall we dance?" and lovingly kisses him right in the mouth. Now wide awake, Daffy wipes the kiss away disgustedly and runs away. The lady pig says "I love that duck!" and laughs before iris out.