RGB-T salient object detection (SOD) aims to accurately locate the most prominent regions in an image by leveraging the complementary information from RGB and thermal modalities. Existing methods mainly rely on CNNs or Transformer-based architectures, which either lack long-range modeling (CNNs) or incur high computational costs (Transformers). In contrast, the recently proposed Mamba and its vision extension VMamba offer an efficient alternative by balancing global context modeling with lower complexity. Inspired by this, we propose a novel RGB-T SOD framework called ViSSNet (Vision State-Space Saliency Network). Specifically, we design a dual-stream VMamba encoder to extract modality-specific features from RGB and thermal inputs. These features are then refined using a State-Space Interactive Fusion Module (SSIFM), which combines the strengths of state-space modeling and convolutional operations to enhance cross-modal representation. Furthermore, a top-down decoding architecture is adopted to progressively integrate high-level semantics with spatial detail, enabling more accurate saliency prediction. Extensive experiments on three public RGB-T SOD benchmarks demonstrate that ViSSNet outperforms 14 state-of-the-art methods, achieving superior or comparable accuracy with significantly reduced model parameters and computational cost.