The large diffusion of Unmanned Aircraft Systems (UAS) requires a suitable strategy to design safe flight missions. In this paper, we propose a novel path planning strategy to compute optimum risk path for UAS over populated areas. The proposed strategy is based on a variant of the RRT* (Rapidly-exploring Random Tree "Star") algorithm, performing a risk assessment during the path planning phase. Like other RRT-based algorithms, the proposed path planning explores the state space by constructing a graph. Each time a new node is added to the graph, the algorithm estimates the risk level involved by the new node, evaluating the flight direction and velocity of the UAS placed in the analyzed node. The risk level quantifies the risk of flying over a specific location and it is defined using a probabilistic risk assessment approach taking into account the drone parameters and environmental characteristics. Then, the proposed algorithm computes an asymptotically optimal path by minimizing the overall risk and flight time. Simulation results in realistic environments corroborate the proposed approach proving how the proposed risk-based path planning is able to compute an effective and safe path in urban areas.