Indite looks like a misspelling of its homophone indict, meaning "to charge with a crime," and that's no mere coincidence. Although the two verbs are distinct in current use, they are in fact related etymologically. "Indite" is the older of the two; it has been in the language since the 1300s. "Indict," which came about as an alteration of "indite," first appeared in English legal use around 1600. Ultimately, both terms come from the Latin indicere, meaning "to make known formally" or "to proclaim," which in turn comes from "in-" plus dicere, meaning "to say."
Middle English enditen, from Anglo-French enditer to write, compose, from Vulgar Latin *indictare, frequentative of Latin indicere to make known formally, proclaim, from in- + dicere to say — more at diction