Smart mobility systems represent a new generation of transport systems that are strongly supported by information and communications technologies, allowing a continuous connection between the system administrators, the customers/users, the transport infrastructures and the vehicles. A major example of these systems is represented by carsharing. Carsharing can relieve people from the costly and non-sustainable burden of owning a car, especially when residing in a city. Furthermore, it can reduce pollution and traffic congestion and has been worldwide recognized by policy-makers as a fundamental component of smart cities. In this study, we provide an overview of relevant regulations for carsharing, highlighting in particular the importance of parking policies. Given this importance, we propose a mathematical optimization model that can be used by a local government to analytically choose the best subset of parking slots to rent to carsharing companies, in order to improve urban mobility. The model corresponds to a Binary Linear Programming problem, which uses binary variables to decide whether a cluster of parking slots is rented or not. It also includes constraints expressing the limits on the number and features of parking slot clusters that can be rented in each city district. We test the model on realistic data of the city of Rome, showing that we can obtain a fair territorial distribution of the parking slots that satisfies population needs. The data were defined on the basis of our collaboration with professionals of the electric utility company Enel within E-Go Car Sharing, an electrical vehicle carsharing service established at the University Roma Tre.