Distributed integrated sensing and communication (DISAC) systems are key enablers for 6G networks, offering the capability to jointly track multiple targets using spatially distributed base stations (BSs). A fundamental challenge in DISAC is the seamless and efficient handover of target tracks between BSs with partially overlapping fields of view, especially in dense and dynamic environments. In this paper, we propose a novel target handover framework based on belief propagation (BP) for multi-target tracking in DISAC systems. By representing the probabilistic data association and tracking problem through a factor graph, the proposed method enables efficient marginal inference with reduced computational complexity. Our framework introduces a principled handover criterion and message-passing strategy that minimizes inter-BS communication while maintaining tracking continuity and accuracy. We demonstrate that the proposed handover procedure achieves performance comparable to centralized processing, yet significantly reduces data exchange and processing overhead. Extensive simulations validate the robustness of the approach in urban tracking scenarios with closely spaced targets.