Video anomaly detection is a fundamental task in video surveillance, with broad applications in public safety and intelligent monitoring systems. Although previous methods leverage Euclidean representations in RGB or depth domains, such embeddings are inherently limited in capturing hierarchical event structures and spatio-temporal continuity. To address these limitations, we propose HyPCV-Former, a novel hyperbolic spatio-temporal transformer for anomaly detection in 3D point cloud videos. Our approach first extracts per-frame spatial features from point cloud sequences via point cloud extractor, and then embeds them into Lorentzian hyperbolic space, which better captures the latent hierarchical structure of events. To model temporal dynamics, we introduce a hyperbolic multi-head self-attention (HMHA) mechanism that leverages Lorentzian inner products and curvature-aware softmax to learn temporal dependencies under non-Euclidean geometry. Our method performs all feature transformations and anomaly scoring directly within full Lorentzian space rather than via tangent space approximation. Extensive experiments demonstrate that HyPCV-Former achieves state-of-the-art performance across multiple anomaly categories, with a 7\% improvement on the TIMo dataset and a 5.6\% gain on the DAD dataset compared to benchmarks. The code will be released upon paper acceptance.