Modern trams have garnered worldwide attention as an alternative urban rail transit system since they offer advantages such as higher accessibility, convenience, lower construction and maintenance costs compared with subways. Nevertheless, due to the system's characteristics, particularly regarding right-of-way issues, crashes involving trams often lead to severe consequences. This study utilizes traffic crash data from across Japan, including 1,121,299 crashes that occurred from 2019 to 2022, of which 304 were tram involved. The study has two major analyses using random-parameter model with heterogeneity in means: (1) tram-involved crashes' characteristics (vs. non-tram-involved) and (2) factors affecting the probability of fatality in tram crashes. The first analysis' findings suggest that fatalities and crashes at rail crossings are more likely to be associated with tram crashes, while non-tram crashes are more likely to occur during daytime, at intersections, or on narrower lanes. Furthermore, the presence of a median between opposing directions increases the likelihood of a non-tram crash. The second analysis to identify the factors influencing fatality reveals how factors such as the season, lighting conditions, road conditions, crash locations, and the age and category of victims affect the characteristics of tram crashes and fatalities. Specifically, it explains the heterogeneous effects of daytime and intersections on tram crashes, as well as the heterogeneous impacts of rail crossings and densely populated areas on tram fatalities. The findings are expected to assist authorities in formulating strategies to minimize the incidence of tram crashes and related fatalities, potentially saving lives and bringing about economic benefits.