Medical referral (directing patients to the appropriate hospital department) is a complex decision-making process requiring the synthesis of multimodal data, including patient narratives, laboratory indicators, and radiology imaging. While Large Language Models (LLMs) have advanced medical dialogue systems, they struggle with real-world referral tasks due to two primary limitations: (1) Information Overload, where models fixate on high-frequency disease terms while overlooking subtle but critical urgency indicators; and (2) Unstructured Collaboration, where existing multi-agent frameworks rely on loose dialogue that leads to semantic drift and confirmation bias. To address these challenges, we introduce MASGR (Multi-Agent Structured Graph Reasoning), a framework that treats referral not as a classification task but as a structured graph construction problem. MASGR deploys specialized agents to extract evidence from distinct modalities and coordinates them through a clinical reasoning graph. This graph forces agents to establish explicit logical connections between conflicting evidence. Furthermore, we integrate a knowledge-guided arbitration mechanism that prioritizes patient safety rules over standard diagnostic classification. Extensive experiments on real-world medical records demonstrate that MASGR significantly outperforms state-of-the-art LLMs and existing multi-agent systems, particularly in complex cases requiring the balancing of chronic disease management and emergency intervention. The AI contribution lies in the Multi-Agent Structured Graph Reasoning framework that transforms unstructured multi-agent dialogue into a verifiable logical graph construction. The engineering application is demonstrated through its deployment in a complex healthcare decision-making system to optimize the precision of complex medical referrals.

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