In this paper the efficiency of the Spanish Police Service is analysed using Data Envelopment Analysis (DEA). The analysis concentrates on the police activities related to the solving of crimes. The theoretical and empirical study of the police production function under this dimension leads to a consideration of the units analysed as centres which carry out their activities with nonidentical technologies and using common inputs. Accordingly, the multiactivity DEA model developed by Mar Molinero (Journal of the Operational Research Society, 47, 1996, 1273-9) is applied, one that is designed to estimate the efficiency of institutions which face several production functions using shared inputs. The results demonstrate the important differences that exist between the centres with respect to the distinct activities analysed, both as regards the efficiency rates and the factors which determine them.