  A search for $CP$ violation in $D^0 \to \pi^-\pi^+\pi^0$ decays is reported,
using $pp$ collision data collected by the LHCb experiment from 2015 to 2018
corresponding to an integrated luminosity of 6$fb^{-1}$. An unbinned
model-independent approach provides sensitivity to local $CP$ violation within
the two-dimensional phase space of the decay. The method is validated using the
Cabibbo-favoured channel $\D^0 \to \K^-\pi^+\pi^0$ and background regions of
the signal mode. The results are consistent with $CP$ symmetry in this decay.
