Domain adaptive point cloud completion (DA PCC) aims to narrow the geometric and semantic discrepancies between the labeled source and unlabeled target domains. Existing methods either suffer from limited receptive fields or quadratic complexity due to using CNNs or vision Transformers. In this paper, we present the first work that studies the adaptability of State Space Models (SSMs) in DA PCC and find that directly applying SSMs to DA PCC will encounter several challenges: directly serializing 3D point clouds into 1D sequences often disrupts the spatial topology and local geometric features of the target domain. Besides, the overlook of designs in the learning domain-agnostic representations hinders the adaptation performance. To address these issues, we propose a novel framework, DAPointMamba for DA PCC, that exhibits strong adaptability across domains and has the advantages of global receptive fields and efficient linear complexity. It has three novel modules. In particular, Cross-Domain Patch-Level Scanning introduces patch-level geometric correspondences, enabling effective local alignment. Cross-Domain Spatial SSM Alignment further strengthens spatial consistency by modulating patch features based on cross-domain similarity, effectively mitigating fine-grained structural discrepancies. Cross-Domain Channel SSM Alignment actively addresses global semantic gaps by interleaving and aligning feature channels. Extensive experiments on both synthetic and real-world benchmarks demonstrate that our DAPointMamba outperforms state-of-the-art methods with less computational complexity and inference latency.