Aligning large language models (LLMs) with human values is essential for their safe deployment and widespread adoption. Current LLM safety benchmarks often focus solely on the refusal of individual problematic queries, which overlooks the importance of the context where the query occurs and may cause undesired refusal of queries under safe contexts that diminish user experience. Addressing this gap, we introduce CASE-Bench, a Context-Aware SafEty Benchmark that integrates context into safety assessments of LLMs. CASE-Bench assigns distinct, formally described contexts to categorized queries based on Contextual Integrity theory. Additionally, in contrast to previous studies which mainly rely on majority voting from just a few annotators, we recruited a sufficient number of annotators necessary to ensure the detection of statistically significant differences among the experimental conditions based on power analysis. Our extensive analysis using CASE-Bench on various open-source and commercial LLMs reveals a substantial and significant influence of context on human judgments (p<0.0001 from a z-test), underscoring the necessity of context in safety evaluations. We also identify notable mismatches between human judgments and LLM responses, particularly in commercial models within safe contexts.