The title names the two things the novel asks whether they are one: the crime, which Raskolnikov commits as early as Part One, and the punishment, which in the book is not the Siberian sentence but what the crime does to him inwardly, and the suffering he is offered to accept.
In Russian, the noun for crime, prestuplenie, comes from a verb meaning to step beyond a line, and the related verb the book repeats is to overstep, which Raskolnikov wants to know whether he can do: "Will I be able to overstep it or won't I!" After the act, he concludes himself: "I did not overstep, I stayed on this side."
The punishment begins before the court. The day after the crime, at the police station, he feels "a dark feeling of tormenting and endless solitude." The police never gather proof, and the eight-year sentence is milder than expected. What weighs is solitude, disgust, and, in his words to Sonia, the fact that he killed himself: "Was it the old woman I killed? It was myself I killed, and not the old woman!"
The book also shows punishment as accepted suffering: Porfiry says that "in suffering there is an idea," Sonia puts the cypress cross on his chest, and the square, the kiss on the earth, and the confession are the path he takes. There are, therefore, two readings of punishment: the torment that springs from the act itself, or the suffering one chooses and which, in the Epilogue, Sonia's love accompanies. The title does not decide between them.