The paper aims to study the effect of spatial interdependence, among nearby municipalities, on public services efficiency. An empirical analysis on the waste disposal service in 4250 Italian municipalities was carried out to evaluate the efficiency of waste management expenditure, once the impact of positive/negative externalities, of neighbouring local governments, on efficiency levels is isolated. From a methodological point of view, our study extends the spatial stochastic frontier methodology proposed in Fusco & Vidoli (2013) usable only for production analysis, allowing to admit into a cost frontier the spatial autocorrelation among residuals. Ignoring spatial autocorrelation leads to inferential problems violating one of the most important assumption of classical regression models: the non-correlation of the residuals. We found a significant spatial interdependence among neighbouring municipalities in term of cost efficiency, that, thanks to the methodology proposed, has been isolated allowing a discussion on the specific efficiency of municipalities. These results may suggest the need to consider proximity effects in future investigations about the efficiency of waste management and, more generally, of public services.