With growing public safety demands, text-based person anomaly search has emerged as a critical task, aiming to retrieve individuals with abnormal behaviors via natural language descriptions. Unlike conventional person search, this task presents two unique challenges: (1) fine-grained cross-modal alignment between textual anomalies and visual behaviors, and (2) anomaly recognition under sparse real-world samples. While Large Multi-modal Models (LMMs) excel in multi-modal understanding, their potential for fine-grained anomaly retrieval remains underexplored, hindered by: (1) a domain gap between generative knowledge and discriminative retrieval, and (2) the absence of efficient adaptation strategies for deployment. In this work, we propose AnomalyLMM, the first framework that harnesses LMMs for text-based person anomaly search. Our key contributions are: (1) A novel coarse-to-fine pipeline integrating LMMs to bridge generative world knowledge with retrieval-centric anomaly detection; (2) A training-free adaptation cookbook featuring masked cross-modal prompting, behavioral saliency prediction, and knowledge-aware re-ranking, enabling zero-shot focus on subtle anomaly cues. As the first study to explore LMMs for this task, we conduct a rigorous evaluation on the PAB dataset, the only publicly available benchmark for text-based person anomaly search, with its curated real-world anomalies covering diverse scenarios (e.g., falling, collision, and being hit). Experiments show the effectiveness of the proposed method, surpassing the competitive baseline by +0.96% Recall@1 accuracy. Notably, our method reveals interpretable alignment between textual anomalies and visual behaviors, validated via qualitative analysis. Our code and models will be released for future research.