Reinforcement learning (RL) can be used to design smart driving policies in complex situations where traditional methods cannot. However, they are frequently black-box in nature, and the resulting policy may perform poorly, including in scenarios where few training cases are available. In this paper, we propose a method to use RL under two conditions: (i) RL works together with a baseline rule-based driving policy; and (ii) the RL intervenes only when the rule-based method seems to have difficulty handling and when the confidence of the RL policy is high. Our motivation is to use a not-well trained RL policy to reliably improve AV performance. The confidence of the policy is evaluated by Lindeberg-Levy Theorem using the recorded data distribution in the training process. The overall framework is named ``confidence-aware reinforcement learning'' (CARL). The condition to switch between the RL policy and the baseline policy is analyzed and presented. Driving in a two-lane roundabout scenario is used as the application case study. Simulation results show the proposed method outperforms the pure RL policy and the baseline rule-based policy.