This paper aims to test the existence of vertical interactions in terms of public spending between overlapping local jurisdictions in France using a data set of 110 French municipalities and their corresponding departments in 2001 and 2005. To do so, we consider that demand for municipal services is conditioned by the services provided by departments. We then estimate two specifications which allow spatial heterogeneity to be modeled thanks to models with spatial regimes and which are compared with a simple spatial error specification (without spatial heterogeneity). The two estimated spatial regimes models are able to eliminate spatial autocorrelation in the error term. The estimation results show that an appropriate consideration of spatial heterogeneity can lead to new insights. The spatial error specification without regimes reveals a robust complementary demand relationship between services provided by departmental and municipal governments. However, the results provided by the spatial regime models are different. They give evidence of heterogeneity in the nature of vertical spending interactions with independence, complementarity, or substitution between the services offered by the two overlapping jurisdictions.