Previous work on dialogue topic shift detection has primarily focused on shallow local reasoning, overlooking the importance of considering the global historical structure and local details to elucidate the underlying causes of topic shift. To address the above two issues, we introduce the dual-process theory to this task and design a novel Dual-Module Framework DMF (i.e., intuition and reasoning module) for dialogue topic shift detection to emulate this cognitive process. Specifically, the intuition module employs Large Language Models (LLMs) to extract and store the global topic structure of historical dialogue, while the reasoning module introduces a LLM to generate reasoning samples between the response and the most recent topic of historical dialogue, thereby providing local detail explanations for topic shift. Moreover, we distill the dual-module framework into a small generative model to facilitate more precise reasoning. The experimental results on three public datasets show that our DMF outperforms the state-of-the-art baselines.