Accurate CT-MRI registration of the cervical spine is essential for preoperative planning because this region is anatomically complex,highly variable,and vulnerable to injury of the vertebral arteries and spinal cord. However,cervical CT-MRI registration remains underexplored,particularly for rigid-deformable hybrid modeling,and the lack of high-quality annotated multimodal data further limits progress. To address these challenges, we construct and release a comprehensively annotated CT-MRI dataset, R-D-Reg, and propose MSR, a rigid-deformable hybrid registration framework for complex joint structures. Specifically, MSR includes a rigid registration module for independent local rigid alignment of individual vertebrae and a deformable registration module with an MSL block that combines Mamba-based global modeling and Swin Transformer-based local modeling through adaptive gating. The rigid and deformable deformation fields are then fused to generate a hybrid field that better preserves local anatomical consistency. The code and dataset are publicly available at https://github.com/ssc1230609-spec/MSR-registration.