  We show that inflationary models with broken rotational invariance generate
testable off-diagonal signatures in the correlation between the $\mu$-type
distortion and temperature fluctuations of the cosmic microwave background.
More precisely, scenarios with a quadrupolar bispectrum asymmetry, usually
generated by fluctuations of primordial vector fields, produce a nonvanishing
$\mu$-$T$ correlation when $|\ell_1-\ell_2|=2$. Since spectral distortions are
sensitive to primordial fluctuations up to very small scales, a cosmic variance
limited spectral distortion experiment can detect such effects with a high
signal-to-noise ratio.
