Crash type, a key contributory factor of crash injury severity level, is typically included in crash severity models as an explanatory variable. However, certain unobserved factors could influence both the crash type and crash injury severity simultaneously. As such, there could exist an endogenous effect of crash type on crash injury severity. The present paper investigates this hypothesis using data from highway ramp areas. These locations tend to be crash-prone because of the frequent lane changes and speed differentials associated with merging, diverging, and weaving of vehicles at those locations. Conventional approaches used in past ramp safety studies modeled crash type and crash injury severity separately, not addressing the endogenous effect of crash type on crash severity at these locations. In this study, a random parameter recursive bivariate probit model is proposed to model the crash type (hit-object and rollover) and crash injury severity at ramp areas simultaneously and to account for any endogenous effect of crash type. The study used highway crash data from ramp areas at highway located in North Carolina from 2016 to 2018. The results indicate that the proposed model can and does capture the endogenous effect of crash type. The likelihood of injury for a rollover crash would be underestimated if endogeneity were not considered. Other exogenous variables including aberrant driving behavior, safety belt, road surface condition, lighting condition, area type, crash location, and ramp type that affect the type and injury severity of crashes at highway ramp areas were identified. The exogenous variables that are significant only for the crash type, such as vehicle type, and speed limit, were detected to have indirect effects on the crash injury severity. Furthermore, the effects of individual heterogeneity of the explanatory variables are considered. Female drivers and old drivers are statistically significant in the means of random parameters. The findings shed light on the potential need and effectiveness of prospective traffic management and control measures to mitigate crash risk at highway ramp areas.