Lewis & Short

K, k, was used in the oldest period of the language as a separate character for the sound k, while C was used for the sound g. In course of time the character C came to be used also for the k sound, and, after the introduction of the character G, for that alone, and K disappeared almost entirely from the Latin orthography, except at the beginning of a few words, for each of which, also, the letter K itself was in common use as an abbreviation; thus, Kæso (or Cæso), Kalendæ (less correctly Calendæ), sometimes Karthago (or Kar.; v. Carthago); and in special connections, Kalumnia, Kaput (for Calumnia and Caput, e. g. k. k. = calumniae causā in jurid. lang.): nam k quidem in nullis verbis utendum puto, nisi quae significat, etiam ut sola ponatur, Quint. 1, 7, 10; cf. id. 1, 4, 9.
Some grammarians, indeed, as early as Quintilian’s time, thought it proper always to write K for initial C before a, Quint. 1, 7, 10.
Besides the above-mentioned abbreviations, the K is also found in KA. for capitalis, KK. for castrorum, K. S. for carus suis.