Large Language Models (LLMs) have demonstrated remarkable capabilities in natural language processing tasks, yet their application to graph structure analysis, particularly in community search, remains underexplored. Community search, a fundamental task in graph analysis, aims to identify groups of nodes with dense interconnections, which is crucial for understanding the macroscopic structure of graphs. In this paper, we propose GraphCS, a comprehensive benchmark designed to evaluate the performance of LLMs in community search tasks. Our experiments reveal that while LLMs exhibit preliminary potential, they frequently fail to return meaningful results and suffer from output bias. To address these limitations, we introduce CS-Agent, a dual-agent collaborative framework to enhance LLM-based community search. CS-Agent leverages the complementary strengths of two LLMs acting as Solver and Validator. Through iterative feedback and refinement, CS-Agent dynamically refines initial results without fine-tuning or additional training. After the multi-round dialogue, Decider module selects the optimal community. Extensive experiments demonstrate that CS-Agent significantly improves the quality and stability of identified communities compared to baseline methods. To our knowledge, this is the first work to apply LLMs to community search, bridging the gap between LLMs and graph analysis while providing a robust and adaptive solution for real-world applications.