Support structures are crucial to laser fusion metal additive manufacturing processes for their capacity for load bearing and heat transfer during the process. While topology optimization has been extensively used to design parts optimized for additive manufacturing, it has not been extended to optimizing support structures to manage distortion and tolerance errors. In this paper, based on the thermal strains during the AM process, topology optimization is applied to support structures to minimize the distortion of flat features of the part geometry, thus minimizing flatness form tolerance error while generating minimal support structures that satisfy the self-support criterion. The inherent strain method is used to calculate the distortion from the additive manufacturing process, and a density-based topology optimization scheme is developed, where the adjoint method is used to derive sensitivities for the distortion-based objective function. The algorithm is applied to representative part geometries to create minimal support structures while minimizing flatness errors of planar features. The distortion obtained using the generated supports resulted in less overall part distortion and improved flatness errors compared to regular column supports. This research presents a promising method for optimizing support structures to minimize GD&T errors of part features.