Research on determination of spatial patterns in urban car accidents plays an important role in improving urban traffic safety. While traditional methods of spatial clustering of car accidents mostly rely on the two dimensional assumption, many spatial events defy this assumption. For instance, car accidents are constrained by the road network and rely on the one dimensional assumption of street network. The aim of this study is to detect and statistically prioritize the car accident-prone segments of an urban road network by a network-based point pattern analysis. The first step involves estimating the density of car accidents in the one dimensional space of the road network using the network kernel density estimation (NKDE) method with equal-split continuous and discontinuous kernel functions. In the second step, due to the lack of statistical prioritization of the accident-prone segments with NKDE method, the output of the NKDE method is integrated with network-constrained Getis-Ord Gi* statistics to measure and compare the accident-prone segments based on the statistical parameter of Z-Score. The integration of these two methods can improve identification of accident-prone segments which is effective in the enhancing of urban safety and sustainability. These methods were tested using the data of damage car accidents in Tehran District 3 during 2013–2017. We also performed the Network K-Function to display the significant clustering of damage car accident points in the network space at different scales. The results have demonstrated that the damage car accidents are significantly clustered.