Two different types of shape resonance states, π* and σ*, formed in the low-energy electron attachments to the low-lying tautomers of DNA bases (adenine, guanine, thymine, and cytosine) in the gas phase are investigated using the quantum scattering method with the non-empirical model potentials in a symmetry-adapted, single-center expansion. Four and three π* states are predicted for purines and pyrimidines, respectively. Comparing the different tautomers of a certain DNA base, we find distinct differences both in the resonance energies and the resonant wave function patterns of π* states. As for the lowest three π* states, the energetic values predicted in this work are also compared with the theoretical and experimental results available in the literature.