Administrative language of Muslim rulers was usually Persian. But I doubt Tipu's courts used Persian. Was it Persian or Kannada? Even the Nizams started using Urdu instead of Persian after the 1800s.
According to the Wikipedia page on Tipu Sultan, he made Persian the official language throughout his kingdom.
This seems to be confirmed in Language in South Asia, by Braj B. Kachru, Yamuna Kachru, & S. N. Sridhar:
Parts of South India came under Muslim rule in various periods, especially during the reign of the Bahamani kings in Andrha Pradesh and north Karnataka, and that of Hyder Ali and Tippu Sultan [sic] in south Karnataka. During the Latter period (eighteenth century), Persian was the official language of the princely state of Mysore, with official records being kept in that language.