Although Gaussian scene representation has achieved remarkable success in tracking and mapping, most existing methods are confined to single-agent systems. Current multi-agent solutions typically rely on centralized architectures, which struggle to account for communication bandwidth constraints. Furthermore, the inherent depth ambiguity of 3D Gaussian splatting poses notable challenges in maintaining geometric consistency. To address these challenges, we introduce CoMA-SLAM, the first distributed multi-agent Gaussian SLAM framework. By leveraging 2D Gaussian surfels and robust initialization strategy, CoMA-SLAM enhances tracking accuracy and geometry consistency. It efficiently manages communication bandwidth while dynamically scaling with the number of agents. Through the integration of intra- and inter-loop closure, distributed keyframe optimization and submap centric update, our framework ensures global consistency and robustly alignment. Synthetic and real-world experiments demonstrate that CoMA-SLAM outperforms state-of-the-art methods in pose accuracy, rendering fidelity, and geometric consistency while maintaining competitive efficiency across distributed multi-agent systems. Notably, by avoiding data transmission to a centralized server, our method reduces communication bandwidth by 99.8% compared to centralized approaches.