  We show that, the decoherence phenomena applied to the neutrino system could
lead us to have an observable breaking of the fundamental CPT symmetry. We
require a specific textures of non-diagonal decoherence matrices, with non-zero
$\delta_{CP}$, for having such observations. Using the information from the CPT
conjugate channels: $\nu_{\mu} \rightarrow \nu_{\mu}$ and $\bar{\nu}_{\mu}
\rightarrow \bar{\nu}_{\mu}$ and its corresponding backgrounds, we have
estimated the sensitivity of DUNE experiment for testing CPT under the previous
conditions. Four scenarios for energy dependent decoherence parameters
$\Gamma_{E_\nu}=\Gamma \times (E_\nu/\mathrm{GeV})^n$, $n=-1,0,1,$ and $2$ are
taken into account, for most of them, DUNE is able to achieve a 5$\sigma$
discovery potential having $\Gamma$ in $\mathcal{O} (10^{-23}$ GeV) for
$\delta_{CP}=3\pi/2$. Meanwhile, for $\delta_{CP}=\pi/2$ we reach 3$\sigma$ for
$\Gamma$ in $\mathcal{O} (10^{-24}$ GeV).
