c. 1600, "neglecting one's duty;" in law, "not in accord with one's moral duty," 1660s, from Medieval Latin inofficiosus "contrary to duty; harmful," from in- "not, opposite of" (see in- (1) + Latin officiosus "dutiful, obliging" (see officious).
word-forming element meaning "not, opposite of, without" (also im-, il-, ir- by assimilation of -n- with following consonant, a tendency which began in later Latin), from Latin in- "not," cognate with Greek an-, Old English un-, all from PIE root *ne- "not."
In Old French and Middle English often en-, but most of these forms have not survived in Modern English, and the few that do (enemy, for instance) no longer are felt as negative. The rule of thumb in English has been to use in- with obviously Latin elements, un- with native or nativized ones.
1560s, "zealous, attentive, eager to serve," from Latin officiosus "full of courtesy, dutiful, obliging," from officium "duty, service" (see office). Sense of "meddlesome, doing more than is asked or required" had emerged by 1600 (in officiously). An officious lie (1570s) is one told to do good to another person (from Latin mendacium officiosum or French mensonge officieux). Related: Officiousness.
<a href="https://www.etymonline.com/word/inofficious">Etymology of inofficious by etymonline</a>
Harper, D. (n.d.). Etymology of inofficious. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/inofficious