  We investigate parity-violating signatures of temperature and polarization
bispectra of the cosmic microwave background (CMB) in an inflationary model
where a rolling pseudoscalar produces large equilateral tensor non-Gaussianity.
By a concrete computation based on full-sky formalism, it is shown that
resultant CMB bispectra have nonzero signals in both parity-even $(\ell_1 +
\ell_2 + \ell_3 = {\rm even})$ and parity-odd $(\ell_1 + \ell_2 + \ell_3 = {\rm
odd})$ spaces, and are almost uncorrelated with usual scalar-mode equilateral
bispectra. These characteristic signatures and polarization information help to
detect such tensor non-Gaussianity. Use of both temperature and E-mode
bispectra potentially improves of $400\%$ the detectability with respect to an
analysis with temperature bispectrum alone. Considering B-mode bispectrum, the
signal-to-noise ratio may be able to increase by 3 orders of magnitude. We
present the $1\sigma$ uncertainties of a parameter depending on a coupling
constant and a rolling condition for the pseudoscalar expected in the ${\it
Planck}$ and the proposed PRISM experiments.
