Zirconia Toughened Alumina (ZTA) a ceramic based composite material has gained more attention from aerospace and biomedical industries to make parts of implants, combustion parts, armour, and inserts. This is because of its mechanical properties especially toughness and hardness which are admirable. Unpleasant machining behaviour retards the ZTA applications. Laser trepan drilling (LTD) is a thermal energy-based drilling process that is used to make macro-sized hole in difficult-to-machine materials. The present paper revealed the optimum values of processing parameters to optimize the material characteristics, namely recast layer thickness and microcrack width. The processing parameters are taken as laser pulse width, pulse frequency, speed and assist gas pressure. The mathematical relationship between the processing parameters and material characteristics is developed using an artificial neural network. The optimum values of processing parameters for the considered material characteristics are validated with a confirmation test. An overall variation of 12% and individual variation of 18.79% and 5.29% were found in both characteristics at the optimum level of processing parameters.