Diagnosability is an important issue in the design of diagnostic systems, because it helps identify whether sufficient information is available to distinguish all the faults. Diagnosability of hybrid systems, however, is challenging, because mode transitions may occur during fault isolation. We present an event-based framework for hybrid systems diagnosis based on a qualitative abstraction of measurement deviations from nominal behavior. We derive event-based fault models that describe the possible measurement deviations sequences due to faults, which, coupled with the mode transition structure of the system, are used to automatically synthesize an event-based diagnoser for hybrid systems. We introduce notions of diagnosability for hybrid systems and show how the event-based diagnoser can be used to verify the diagnosability of the system. We apply our diagnosability analysis scheme to a real-world electrical power distribution system.