Human-centric perception with radio frequency (RF) signals has recently entered a new era of end-to-end processing with Transformers. Considering the long-sequence nature of RF signals, the State Space Model (SSM) has emerged as a superior alternative due to its effective long-sequence modeling and linear complexity. However, integrating SSM into RF-based sensing presents unique challenges including the fundamentally different signal representation, distinct frequency responses in different scenarios, and incomplete capture caused by specular reflection. To address this, we carefully devise a dual-branch SSM block that is characterized by adaptively grasping the most informative frequency cues and the assistant spatial information to fully explore the human representations from radar echoes. Based on these two branchs, we further introduce an SSM-based network for handling various downstream human perception tasks, named RFMamba. Extensive experimental results demonstrate the superior performance of our proposed RFMamba across all three downstream tasks. To the best of our knowledge, RFMamba is the first attempt to introduce SSM into RF-based human-centric perception.