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Accurate and computationally efficient 3D medical image segmentation remains a critical challenge in clinical workflows. Transformer-based architectures often demonstrate superior global contextual modeling but at the expense of excessive parameter counts and memory demands, restricting their clinical deployment. We propose RefineFormer3D, a lightweight hierarchical transformer architecture that balances segmentation accuracy and computational efficiency for volumetric medical imaging. The architecture integrates three key components: (i) GhostConv3D-based patch embedding for efficient feature extraction with minimal redundancy, (ii) MixFFN3D module with low-rank projections and depthwise convolutions for parameter-efficient feature extraction, and (iii) a cross-attention fusion decoder enabling adaptive multi-scale skip connection integration. RefineFormer3D contains only 2.94M parameters, substantially fewer than contemporary transformer-based methods. Extensive experiments on ACDC and BraTS benchmarks demonstrate that RefineFormer3D achieves 93.44\% and 85.9\% average Dice scores respectively, outperforming or matching state-of-the-art methods while requiring significantly fewer parameters. Furthermore, the model achieves fast inference (8.35 ms per volume on GPU) with low memory requirements, supporting deployment in resource-constrained clinical environments. These results establish RefineFormer3D as an effective and scalable solution for practical 3D medical image segmentation.