If you believe Cicero's In Verrem, Verres, governor of Sicily, certainly serves as an example for a mad type. According to Cicero's accusation Verres stole not just from the people of Sicily, but also from the temples (of Roman gods) and even the gifts former famous generals (like Scipio Africanus) gave to cities. He further took money for himself, that was meant to keep up the naval forces in Sicily and also neglected the rules of how many troops all citys had to send.

Despite that, Cicero writes, that Verres raped all young women whereever he came and after that even made sure that the male relatives got executed because they tried to defend their family's honor. Additional he tortured many of the noble people in Sicily and on top of all even crucified a Roman citizen. While the stealing was usual practice of Roman governors to some degree, he overdid and he committed one of the biggest crimes by executing a Roman citizen. Cicero completes the picture of a mad men by showing the character of Verres (although we can't know for sure how far this is true). According to Cicero he behaved more like an oriental princess than like a Roman governor. Most of the times he spent in his palace or in a luxurious tent, but when he travelled around Sicily, like it was his duty, he is said to be carried in a sedan sitting on a pillow filled with roses and wearing a veil in front of his face (just like a princess would do).

There is more to it, that i am willing to answer if you have more questions, but i think this gives you an impression and also is one of if not the most famous example for a mad governor in ancient Rome.