Nonparametric assessments of police technical and scale efficiency is challenging because of the stochastic nature of criminal behavior and because of the subjective dependence on multiple decision criteria, which can lead to a more or less efficiency prospect depending on the regulation, necessity, or organizational objective. There is a trade-off between efficiency and effectiveness in many police performance assessments, i.e., efficient departments (producing more clear-ups with a given resource) are crime-specialized or cannot reproduce those good results effectively on more severe or complex occurrences. This study proposes a combined methodology for carrying out efficiency and effectiveness analysis of Police departments. A conditional non-parametric approach, which allows to include crime as an external factor in the analysis, is combined with a non-compensatory ranking based on the PROMETHEE II methodology for the approach illustrated on the multidimensional efficiency and effectiveness comparison of 145 Pernambuco (Brazil)'s police departments. The application results offer compelling perspectives for public administrations concerning the strategic prioritization of units for rewards or interventions.