Vehicle automation, manifested in self-driving cars, promises to provide safe mobility by reducing human errors. While the testing of automated vehicles (AVs) has improved their performance in recent years, automation technologies face challenges such as uncertainty of safety impacts in mixed traffic with human-driven vehicles. This study aims to examine the gaps in AV safety performance and identify what will be required on a preferential basis for AVs to guarantee an acceptable level of safety performance, especially in mixed traffic, by conducting a thorough analysis of crashes involving levels 2–3 AVs. Based on 260 AV collision reports from California from 2019 to 2021, this study extracts crash-related variables from crash records in a standardized form, crash locations, and, notably, crash narratives reported by AV manufacturers. This study untangles the complex interrelationships among pre-crash conditions, AV driving modes, crash types, and crash outcomes by applying a path-analytic framework with the frequentist and Bayesian approaches. Results show that 51.9 percent of crashes were rear-ends. Particularly, AVs become more vulnerable to rear-end collisions in the automated driving mode than in the conventional mode, given a crash. Additionally, the automated driving mode would not significantly affect the chance of a sideswipe collision, injury, or AV damage levels. Another interesting finding is that manual disengagement is more likely to happen when an AV interacts with a transit vehicle right before a crash occurs while having a negative relationship with injury crashes. Moreover, to reduce injury crashes, AVs would need more thorough testing to adapt to the critical roadway and infrastructure features such as intersections, ramps, and slip lanes; and roadway infrastructure would require improvements to support transportation automation. The risk factors identified in this study can be considered in AV safety assessment scenarios and future operations of mixed traffic. This study demonstrates that AV crash narrative data can be leveraged to improve knowledge of AV safety in mixed traffic.