The study of the relationship between crude oil and its refined products prices may be perceived as an important tool for testing how are the dynamics and the type of integration of the petro-derivatives market in the United States. In this sense, we have applied a set of causality tests to study the possible presence of asymmetries in the relationship between WTI crude oil and each refined product price and to explore the type of market integration. Furthermore, the application of these causality tests lets us explore the validation of different hypotheses in the literature, such as the Rocket and Feathers hypothesis and the Verleger hypothesis. Our findings reveal that Reformulated Gasoline Blendstock for Oxygen Blending (RBOB), heating oil, diesel and kerosene are supply-driven integrated and conventional gasoline and kerosene are demand-driven integrated when linear effects are assessed. This behaviour changes deeply when the existence of asymmetries is tested, noticing that the Rocket and Feathers hypothesis is not fulfilled when a negative shock appears. Conversely, the Verleger hypothesis is supported when a negative shock appears for conventional gasoline and kerosene. These results provide important policy implications for investors, energy policymakers and refiners.