We present a deep learning method that propagates point-wise feature representations across shapes within a collection for the purpose of 3D shape segmentation. We propose a cross-shape attention mechanism to enable interactions between a shape's point-wise features and those of other shapes. The mechanism assesses both the degree of interaction between points and also mediates feature propagation across shapes, improving the accuracy and consistency of the resulting point-wise feature representations for shape segmentation. Our method also proposes a shape retrieval measure to select suitable shapes for cross-shape attention operations for each test shape. Our experiments demonstrate that our approach yields state-of-the-art results in the popular PartNet dataset.