Three generations of the Leonides family live together in a large, seemingly crooked house, under the patriarchy of Aristide, an ageing millionaire who spends his remaining days in the company of his second wife Brenda, fifty years his junior. After the old man is poisoned with his own eye medicine (eserine), his granddaughter Sophia tells her fiancee Charles Hayward, the story's first person narrator, that she can't marry him until the killer is apprehended; so, desperate for her hand in marriage, he begins his own investigation...
The first person narrator is Charles Hayward who, towards the end of the Second World War, occupies some post in Cairo. There he meets Sophia Leonides, a smart, successful young Englishwoman who works for the Foreign Office. They fall in love, but put off getting engaged until after the end of the war when they will be reunited in England.
Hayward returns home only to find an obituary in The Times: Sophia's grandfather, the wealthy entrepreneur Aristide Leonides, has died, aged 85. Due to the war, the whole family has been living with him in a sumptuous but ill-proportioned house called "Three Gables"–the 'crooked house' of the title. When the autopsy reveals that Aristide Leonides has been poisoned with his own eserine-based eye medicine via an insulin injection, Sophia tells Charles that she can't marry him until the matter is cleared up.
The obvious suspects are Brenda Leonides, Aristide's much younger second wife, and Laurence Brown, a conscientious objector who has been living in the house as private tutor to Eustace and Josephine, Sophia's younger brother and sister. Rumour has it that Brenda and Laurence have been carrying on an illicit love affair right under old Leonides's nose. All the family members hope these two prove to be the murderers because they despise Brenda as a gold digger and also hope to escape the scandal that a different outcome would bring. When police interviews fail to turn up a clear suspect, Charles agrees to help his uncle, an Assistant Commissioner of Scotland Yard, investigate the crime. He becomes a house guest at Three Gables, hoping that someone might reveal a clue at an unguarded moment.
All the family members had motive and opportunity, none has an alibi, and everyone knew that Aristide's eye medicine was poisonous. Moreover, according to the will of record, they all stand to gain a healthy bequest from the old man's estate. Aside from this, the family members have little in common. Edith de Haviland, Aristide's unmarried sister-in-law, is a repressed, somewhat bitter woman who came to stay with him after his first wife's death in order to supervise his children's upbringing. Roger, the eldest son and always Aristide's favourite, is a failure as businessman and has steered the catering business bestowed to him by his father to the brink of bankruptcy; he longs to live a simple life somewhere far away. Roger's wife Clemency, a scientist with austere tastes, has never been able to enjoy the wealth offered by her husband's family. Philip, Roger's younger brother, has suffered all his life under his father's preference for Roger and retreated into a distant world of books and bygone historical epochs, spending all his waking hours in the library of the house. Philip's wife Magda is a modestly successful actress to whom everything, even a murder in the family, is a stage show in which she wants to play a leading part. Sixteen-year-old Eustace still suffers from the aftereffects of a mild case of polio, but otherwise is an average sort of boy. His twelve-year-old sister Josephine, on the other hand, is ugly, odd, precociously intelligent, and so obsessed with detective stories that she spies continually on the rest of the household, writing down her observations in a secret notebook.
Things get complicated when it is revealed that Leonides secretly redrafted his will to leave everything to Sophia because he believed that only she had the strength of character to assume his place as the head of the family. Next, Josephine–who has been bragging that she knows the killer's identity–is found lying in the yard, unconscious from a severe blow to the head from a marble doorstop. At this point, Charles discovers a cache of incriminating love letters from Brenda to Laurence, and the two are arrested. While they are in custody, however, the children's nanny dies after drinking a digitalis-laced cup of cocoa that had apparently been intended for Josephine, and the family realizes that the killer is still among them.
Charles, afraid for Josephine's life, tries in vain to induce her to tell him the murderer's name. Afterwards, Edith de Haviland invites the girl to come out with her in the car for an ice cream soda—then drives over a cliff. Both die instantly.
Back at Three Gables, Charles finds two letters from de Haviland: one is a suicide note for Chief Inspector Taverner confessing to the murders of Aristide, the nanny, and Josephine. The other letter, intended for Charles's eyes only, reveals the truth of the matter - Josephine is the murderer. As proof, de Haviland has enclosed the child's secret notebook, the first line of which reads "To-day I killed grandfather." It is revealed that she committed the murder simply because her grandfather wouldn't pay for her ballet lessons; she then revelled in all the attention she received afterwards and planned her own assault with the marble doorstop as a way of diverting attention. She poisoned Nannie for encouraging Magda to send her to Switzerland, and also because she despised her for calling her a 'silly little girl'. Edith discovered Josephine's notebook hidden in a dog kennel, and killed them both because she didn't want her to suffer when the police discovered the truth.
No review of this book appeared in the Times Literary Supplement.
Maurice Richardson, in the May 29, 1949 issue of The Observer gave a positive review in comparison to his opinion of Taken at the Flood the previous year: "Her forty-ninth book and one of her best seven. Poisoning of aged iniquitous anglicised Levantine millionaire. Nicely characterised family of suspects. Delicious red herrings. Infinite suspense and shocking surprise finish make up for slight looseness of texture.
An unnamed reviewer in the Toronto Daily Star of March 12, 1949 said, "Chief Inspector Taverner of Scotland Yard was as brilliant as usual but barking up the wrong tree - as Agatha Christie demonstrates in a surprise ending which introduces a novel idea in murder mystery.
Robert Barnard: "'Pure pleasure' was how the author described the writing of this, which was long planned, and remained one of her favourites. As the title implies, this is a family murder – and a very odd family indeed. The solution, one of the classic ones, was anticipated (but much less effectively) in Margery Allingham's 'prentice work The White Cottage Mystery.
A condensed version of the novel was first published in the US in Cosmopolitan magazine in the issue for October 1948 (Volume 125, Number 4) with an illustration by Grushkin.
In the UK the novel was first serialised in the weekly magazine John Bull in seven abridged instalments from April 23 (Volume 85, Number 2234) to June 4, 1949 (Volume 85, Number 2240) with illustrations by Alfred Sindall.