Indite looks like a misspelling of its homophoneindict, 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 English language since the 1300s. Indict, which came about as an alteration of indite, appeared in the 16th century. Ultimately, both terms come from Latin indicere, meaning "to make known formally" or "to proclaim," which in turn comes from in- plus dīcere, meaning "to talk, speak, or 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