This paper proposes a reconfigurable planar metamaterial that can be switched between capacitive and inductive responses using local changes in the electrical conductivity of its constituent material. The proposed device is based on Babinet's principle and exploits the singular electromagnetic responses of metallic checkerboard structures, which are dependent on the local electrical conductivity. Utilizing the heating-induced metal-insulator transition of vanadium dioxide (VO2), the proposed meta-material is designed to compensate for the effect of the substrate and is experimentally characterized in the terahertz regime. This reconfigurable metamaterial can be utilized as a switchable filter and as a switchable phase shifter for terahertz waves.