Despite recent advances in reinforcement learning (RL), its application in safety critical domains like autonomous vehicles is still challenging. Although punishing RL agents for risky situations can help to learn safe policies, it may also lead to highly conservative behavior. In this paper, we propose a distributional RL framework in order to learn adaptive policies that can tune their level of conservativity at run-time based on the desired comfort and utility. Using a proactive safety verification approach, the proposed framework can guarantee that actions generated from RL are fail-safe according to the worst-case assumptions. Concurrently, the policy is encouraged to minimize safety interference and generate more comfortable behavior. We trained and evaluated the proposed approach and baseline policies using a high level simulator with a variety of randomized scenarios including several corner cases which rarely happen in reality but are very crucial. In light of our experiments, the behavior of policies learned using distributional RL can be adaptive at run-time and robust to the environment uncertainty. Quantitatively, the learned distributional RL agent drives in average 8 seconds faster than the normal DQN policy and requires 83\% less safety interference compared to the rule-based policy with slightly increasing the average crossing time. We also study sensitivity of the learned policy in environments with higher perception noise and show that our algorithm learns policies that can still drive reliable when the perception noise is two times higher than the training configuration for automated merging and crossing at occluded intersections.