There is no official line. The most quoted one from outside, "if God does not exist, everything is permitted," is not in the book in those words and has an answer of its own. Within the book, three sentences concentrate what it says: it is not God I refuse, I merely return to Him, with the greatest respect, my ticket; each one is guilty before all, for all and for everything; and here the devil fights with God, and the battlefield is the hearts of men.
The first is Ivan's, in Book V, chapter IV, "Rebellion." After speaking of the suffering of children, he tells Alyosha that he is hurrying to return his ticket of admission: he does not refuse God, he returns the ticket. It is the refusal of a final harmony paid for with the tears of a child. Alyosha gives this the name of rebellion, and Ivan does not want the word: can one live on rebellion? he asks, and says he wants to live.
The second has its origin in Zosima's biography. In Book IV, chapter I, he says it to the monks at his farewell; in Book VI, chapter II, the book shows where it comes from: his brother Markel, sick, answers his mother that each one is guilty before all, for all and for everything, and feels this to the point of torment. Mitya repeats it in Book XI, chapter IV, when he explains why he will go to Siberia for the sake of the boy in the dream, even without having killed his father. It is the sentence that gives its name to Zosima's doctrine, and the novel carries it from the cell to the prison.
The third is Mitya's, in Book III, chapter III, when he confesses to Alyosha in verse what he feels: beauty is a terrible and frightening thing, and there the devil fights with God, and the battlefield is the hearts of men. He himself disarms the grandeur soon after, saying that each one speaks of what hurts him, so that the sentence reads either as a thesis about man or as a justification of a pain he refuses to call guilt.