Scholars have proposed a series of methods, such as “sustainability of local government debt”, to measure local government debt risks. However, these methods have caused a lot of controversy. Based on a macro balance sheet, this study uses an improved “distance to distress” to measure China’s local government debt risks and applies a social network model to identify the spatial correlation characteristics, as well as the spillover effect. The results are as follows: (1) The data show multiple and heterogeneous spatial correlations for China’s local government debt risks; (2) there are some similarities between the subgroups and seven major geographic regions in China. The links among subgroups are randomly distributed and external; (3) the data manifest a “small world”, with a decreasing transitivity since 2014; (4) between these two significant factors, the positive impact of local government competition is more obvious than the division of powers and responsibilities; and (5) the spatial spillover effect of China’s local government debt risks results from the combination of local government competition, the division of powers and responsibilities, and local government intervention. This paper provides a scientific basis for obtaining a deeper understanding of China’s local government debt risks, and puts forward policy recommendations to strengthen China’s debt management.