We study an inflationary scenario with a two-form field to which an inflaton couples non-trivially. We show that the two-form hair remains during inflation. Consequently, a statistical anisotropy can be developed because of a cumulative anisotropic interaction induced by the background two-form field. The power spectrum of curvature perturbations has a prolate-type anisotropy, in contrast to the vector models having an oblate-type anisotropy. We also evaluate the bispectrum and trispectrum of curvature perturbations by employing the in-in formalism based on the interacting Hamiltonians. We find that the non-linear estimators fNL and τNL are correlated with the amplitude g∗ of the statistical anisotropy in the power spectrum.