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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 …