1670s, "person arraigned for a crime or offense," according to legal tradition from Anglo-French cul prit, a contraction of Culpable: prest (d'averrer nostre bille) "guilty, ready (to prove our case)," words used by prosecutor in opening a trial. See culpable. It seems the abbreviation cul. prit was mistaken in English for an address to the defendant.
Meaning "a criminal, an offender" (1769) is, according to OED, "A change of sense, apparently due to popular etymology, the word being referred directly to L. culpa fault, offense."
late 14c., "injurious, dangerous," also "absurd, illogical" (senses now obsolete), from Latin inconvenientem (nominative inconveniens) "unsuitable, not accordant, dissimilar," from in- "not, opposite of" (see in- (1)) + convenientem (see convenient). In early 15c., "inappropriate, unbecoming, unnatural;" also, of an accused person, "unlikely as a culprit, innocent." Sense of "troublesome, incommodious, awkward" is recorded from 1650s.