Abdominal organ segmentation is a fundamental and essential task for abdominal disease diagnosis, cancer treatment, and radiation therapy planning. Accurate segmentation results can provide valuable information for clinical diagnosis and follow-up, such as organ size, location, boundary condition, and spatial relationships among multiple organs. Reliable abdominal organ segmentation is crucial for improving patient care and treatment outcomes. Despite clear anatomical boundaries between organs, accurate abdominal organ segmentation from CT images remains challenging due to case variations, organ deformations, and ambiguous boundaries. Furthermore, the vast volume differences between organs can lead to competitive effects during network training, further complicating the segmentation task. To address the above challenges, this paper presents ReSU-Net, A novel multi-class medical image segmentation model that synergistically combines the strengths of Transformer, State Space Model (SSM), and residual connection. The core component of ReSU-Net is the Residual State Space Module (RSSM), which integrates SSM into a residual structure, enabling efficient encoding of long-range dependencies while capturing multi-scale features. By leveraging the global context modeling capabilities of Transformers, the long-range modeling power of SSM, and the multi-scale feature fusion facilitated by residual connections, ReSU-Net achieves excellent segmentation performance. We evaluate ReSU-Net on the challenging multi-organ segmentation task from abdominal MRI scans using the AbdomenMR dataset. Comprehensive experiments demonstrate the superiority of our proposed model, achieving an average Dice score of 0.8227 and outperforming popular CNN-based and Transformer-based segmentation methods. Qualitative visualizations further highlight the precise delineation capabilities of ReSU-Net, accurately capturing organ boundaries and contours.