"act of conniving, an overlooking of a disreputable or illegal action, often implying private approval," especially, in divorce law, "corrupt consent of a married person to that conduct of the spouse of which complaint is later made," 1590s, from French connivence or directly from Latin conniventia, from conniventem (nominative connivens), present participle of connivere "to wink," hence, "to wink at (a crime), be secretly privy" (see connive). According to OED, the spelling with -a- prevailed after early 18c. but is unetymological.
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Harper, D. (n.d.). Etymology of connivance. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/connivance