1832, Latin, literally "body of the offense;" not "the murder victim's body," but the basic elements that make up a crime, which in the case of a murder includes the body of the victim. For first element, see corpus. With delictum "a fault, offense, crime, transgression," etymologically "a falling short" of the standard of law, neuter singular of past participle of delinquere "to fail; be wanting, fall short; offend" (see delinquent).
Thus, a man who is proved to have clandestinely buried a dead body, no matter how suspicious the circumstances, cannot thereby be convicted of murder, without proof of the corpus delicti--that is, the fact that death was feloniously produced by him. [Century Dictionary]