The entire world is still trying to understand and stop the spread of the COVID-19 disease. It is known that the evolution of human mobility associated with economic, geographic and demographic factors have caused differences in the spatial spread of the new coronavirus in distinct countries and regions and has also contributed to the rapid spread of the disease. The characterization of the spatial patterns of disease spreading involves environmental and social factors. In this context, we used statistical tools to investigate the spatial distribution of the incidence and mortality rates over time in two of the most populous Brazilian states:  São Paulo and Minas Gerais.  Our results show an spatial dependence among micro-regions related to incidence and mortality rates but with different spatial autocorrelations in both states. We used the VAR model to verify this causal relationship among the micro-units that showed spatial dependence. We found that there is a feedback relationship and also causality between some investigated areas. We also show that the heterogeneity of the spatial distribution of ICU beds, associated with the age stratification of the population, can explain the difference of the mortality rate in each subregion. Our findings indicate that government agencies should consider these regional differences when planning specific public health policies for each region.