In this paper a control approach for safe and energy efficient autonomous overtaking is presented. The proposed method combines a stochastic approach based on the use of safety indicators as the Time headway (TH) and Time to collision (TTC) as boundary conditions and a cost index on fuel consumption for the trajectory of an Ego vehicle in a traffic environment. The approach has been evaluated in two typical overtaking scenarios: 1) braking of the leading vehicle and 2) entry of a third vehicle in the gap between the leading and the ego vehicle. The efficiency of TH and TTC- based stochastic approach have been compared for the same maximal risk threshold. Results show that both risk function are suitable to perform overtaking manoeuvres both with and without an additive fuel cost. Moreover the TTC-based stochastic approach shows a reduction of about 5{%} in fuel consumption with respect to the TH-based approach for both considered scenarios.