The irony contained within "A Municipal Report" lies in the relationship between the three main characters as set in the particular location of the story's action. In Nashville, Tennessee in the early 1900's, racial prejudice was still widespread and effective in determining the ways in which persons of different races interacted. In addition, the southern cultural expectations defined certain types of behaviors as being acceptable or forbidden by society.
In the story, Azaela Adair is "a product of the old South, gently nurtured in the sheltered life. Her learning was not broad, but was deep and of splendid originality in its somewhat narrow scope." She is also an author and the wife of "Major" Wentworth Caswell, a violent drunkard who steals any income his wife receives from her writing to finance his drinking habit.
Azaela's savior from this wretched situation is the African-American taxi driver King Cettiwayo and the band of other blacks he led in murdering the "Major." For Azaela to owe her life and future comfort to a black man who was not her slave would be considered highly improper in that setting - irony number one.
A second irony is the cooperation of the story's narrator in covering the evidence of the identity of the murder. The narrator quietly lays claim to the unusual button that drops from the dead "Major" Caswell's hand - the button that the narrator had noted on King Cettiwayo's clothing when paying for the taxi conveyance to meet with Azaela Adair - and throws it into the Cumberland River as he leaves Nashville.