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In this study, an evaluation model is developed to analyze the safety level of a street network in terms of accessibility for emergency services and evacuation risk for residents, especially for cities experiencing rapid urbanization and densification. The evaluation model is created based on the network geometry and street width using the Network Voronoi algorithm, and four evaluation variables are developed, namely the accessibility risk, unreachability risk, edge responsibility, and flow capacity. Next, the model is applied to an alleyway neighborhood in Ho Chi Minh City, characterized by a labyrinthine mesh and tree-shaped network, and narrow street widths. Finally, improvement interventions, such as adding new links and widening alleys, are implemented in three case studies, and the results are compared in terms of cost, social impact, and safety improvement. The results show that the most efficient improvement strategy is to target the weakest point in the network, except for the flow capacity, which, however, can detect intersections at risk on evacuation routes, which cannot be derived from the network topology. The developed evaluation model is not only useful to analyze the current risk level in the network but is also a powerful tool to evaluate future infrastructure improvement projects.