The 2.5D process is widely utilized in modern industries, with multi-genus cross-sections increasingly encountered in both additive and subtractive manufacturing. Tool paths for multi-genus shapes often suffer from discontinuities that lead to frequent tool liftings, and self-intersections in offset paths, adversely affecting machining accuracy and efficiency. In this context, path topology, stepover uniformity, and degeneration of offset paths represent three fundamental concerns that must be considered in an integrated manner in 2.5D path planning for multi-genus shapes. This study proposes a tool path planning method based on combining of topological and geometric characteristics of medial axis transformation for the shape with multi-genus. A region segmentation strategy tailored to multi-genus shapes is first introduced to prevent global self-intersections in equidistant offset paths. Subsequently, the graph structure of the segmented shape is extracted, and the minimization of tool liftings is formulated as a minimum path cover problem in an undirected graph. A Fermat-spiral-like path topology is adopted within sub-regions to preserve the connectivity of graph and ensure smooth transitions between successive layers of contour-parallel paths. Numerical and physical experiment results confirm the proposed method’s effectiveness in maintaining stepover uniformity, avoiding degeneration of global self-intersections, and ensuring path connectivity.