Existing Video Anomaly Detection (VAD) methods typically rely on task-specific training, leading to strong domain dependency and high training costs. Moreover, most existing methods output only scalar anomaly scores, providing limited insight into why specific events are considered abnormal. Recent advances in Vision-Language Models (VLMs) have enabled both anomaly detection and human-interpretable reasoning. However, many VLM-based approaches still require additional training steps (e.g., instruction tuning or verbalized learning) or external Large Language Models (LLMs), incurring further training costs and inference overhead. To address these challenges, we propose CoReVAD, a contextual reasoning framework for training-free video anomaly detection that operates with a single frozen VLM. CoReVAD directly generates anomaly scores and temporal descriptions from the VLM. To mitigate noise in generative outputs, we introduce a Local Response Cleaning (LRC) module based on local vision-text alignment. Furthermore, global temporal context and progression are incorporated through softmax-based refinement, Gaussian smoothing, and position weighting. Experiments on UCF-Crime and XD-Violence demonstrate that CoReVAD achieves competitive performance among training-free methods while providing reliable and interpretable explanations. Our official code is available at: https://github.com/Muk-00/CoReVAD