  We investigate the CMB $\mu$ distortion in models where two uncorrelated
sources contribute to primordial perturbations. We parameterise each source by
an amplitude, tilt, running and running of the running. We perform a detailed
analysis of the distribution signal as function of the model parameters,
highlighting the differences compared to single-source models. As a specific
example, we also investigate the mixed inflaton-curvaton scenario. We find that
the $\mu$ distortion could efficiently break degeneracies of curvaton
parameters especially when combined with future sensitivity of probing the
tensor-to-scalar ratio $r$. For example, assuming bounds $\mu < 0.5 \times
10^{-8}$ and $r<0.01$, the curvaton contribution should either vanish or the
curvaton should dominate primordial perturbations and its slow-roll parameter
$\eta_{\chi}$ is constrained to the interval $-0.007 < \eta_{\chi}< 0.045$.
