On-demand mobility services, such as bike and car sharing, are experiencing an exponential growth and are expected to play an essential role in future transportation systems. In addition, car sharing is recognised as a key driving force for the diffusion of electric vehicles (EVs) in urban areas. The impact of a regulated fleet of shared electric cars on the power distribution grid is expected to be significant and very different from that of privately-owned EVs due to: the different mobility patterns (e.g., higher vehicle utilisation, shorter parking times), and the dependence of charging opportunities on the specific layout of the car-sharing station infrastructure. However, these issues are not sufficiently investigated in the research literature. To fill this gape in this work we make the following two main contributions. First, we formulate a stochastic facility location problem for the optimal deployment of the car sharing stations to provide probabilistic guarantees on parking availability. Second, we analyse the energy demands of the car sharing system under different deployment scenarios and charging technologies, including power sharing. Finally, to test how well our model can be applied to the real world we leverage on a data-driven evaluation methodology based upon the travel demands of an existing car sharing operator.