In this paper, we propose a novel distributed algorithm for cooperative rerouting of Connected and Automated Vehicles (CAVs) in urban networks, in which each intersection unit manages the portion of the network for which they are in charge by sending updated routes to follow to the CAVs therein, while communicating among each other to be updated on the situation of the (in general non-homogeneous) roads of the network. The proposed approach allows to decompose the problem into subproblems, which are resolved distributively with little information exchange. The problems are constructed to obtain a fair compromise between user equilibrium and system performance. We show the results we obtained on a simulated urban network with CAVs and compared them with a baseline scenario.