Given a specific query case, legal case retrieval systems aim to retrieve a set of case documents relevant to the case at hand. Previous studies on user behavior analysis have shown that information retrieval (IR) systems can significantly influence users' decisions by presenting results in varying orders and formats. However, whether such influence exists in legal case retrieval remains largely unknown. This study presents the first investigation into the influence of legal case retrieval systems on the decision-making process of legal users. We conducted an online user study involving more than ninety participants, and our findings suggest that the result distribution of legal case retrieval systems indeed affect users' judgements on the sentences in cases. Notably, when users are presented with biased results that involve harsher sentences, they tend to impose harsher sentences on the current case as well. This research highlights the importance of optimizing the unbiasedness of legal case retrieval systems.