RGB-Event Video Person Re-Identification (RE-VReID) aims to retrieve specific person across non-overlapping cameras with complementary RGB videos and event streams. However, existing methods often decouple spatial and temporal modeling, which limits their interaction. In addition, global-level RGB-Event fusion fails to fully exploit fine-grained discriminative cues. To address these issues, we propose Paths, a unified framework with spatio-temporal modeling and hierarchical multi-modal fusion for RE-VReID. Specifically, we first design a Memory-Augmented Backbone (MAB) to maintain modality-specific identity prototypes for stable intra-modal representation learning. Then, we propose a Prompt-aware Spatio-temporal Transformer (PST) to jointly model spatial and temporal cues within a unified Transformer. Finally, we introduce a Hierarchical Multi-modal Fusion (HMF) to integrate RGB and event features at global and local levels. With these modules, our framework can learn robust and discriminative representations for RE-VReID. Extensive experiments on three public RE-VReID benchmarks including EvReID, MARS and iLIDS-VID, demonstrate the effectiveness of our proposed method. The code is available at https://github.com/Reflection0427/Paths.