"accountable for one's actions, answerable" to another, for an act performed or its consequences, 1640s, from obsolete French responsible (13c., Modern French responsable, as if from Latin *responsabilis), from Latin respons-, past-participle stem of respondere "respond, answer to, promise in return," from re- "back" (see re-) + spondere "to pledge" (see sponsor (n.)).
The meaning "reliable, trustworthy" is from 1690s. It retains the sense of "obligation" in the Latin verb. Related: Responsibly.
With regard to the legal use of the word, two conceptions are often confused — namely, that of the potential condition of being bound to answer or respond in case a wrong should occur, and that of the actual condition of being bound to respond because a wrong has occurred. For the first of these responsible is properly used, and for the second liable. [Century Dictionary]