Several recent transportation safety studies have indicated the importance of accounting for correlated outcomes, for example, among different crash types, including differing injury-severity levels. In this paper, we discuss inference for such data by introducing a flexible Bayesian multivariate model. In particular, we use a Dirichlet process mixture to keep the dependence structure unconstrained, relaxing the usual homogeneity assumptions. The resulting model collapses into a latent class multivariate model that is in the form of a flexible mixture of multivariate normal densities for which the number of mixtures (latent components) not only can be large but also can be inferred from the data as part of the analysis. Therefore, besides accounting for correlation among crash types through a heterogeneous correlation structure, the proposed model helps address unobserved heterogeneity through its latent class component. To our knowledge, this is the first study to propose and apply such a model in the transportation literature. We use the model to investigate the effects of various factors such as built environment characteristics on pedestrian and cyclist injury counts at signalized intersections in Montreal, modeling both outcomes simultaneously. We demonstrate that the homogeneity assumption of the standard multivariate model does not hold for the dataset used in this study. Consequently, we show how such a spurious assumption affects predictive performance of the model and the interpretation of the variables based on marginal effects. Our flexible model better captures the underlying complex structure of the correlated data, resulting in a more accurate model that contributes to a better understanding of safety correlates of non-motorist road users. This in turn helps decision-makers in selecting more appropriate countermeasures targeting vulnerable road users, promoting the mobility and safety of active modes of transportation.