We show that the decoherence phenomena applied to the neutrino system could lead to an observable breaking of the fundamental CPT symmetry. We require specific textures of nondiagonal decoherence matrices, with nonzero δCP, for making such observations. Using the information from the CPT conjugate channels νμ→νμ and νμ→νμ and their corresponding backgrounds, we have estimated the sensitivity of the DUNE experiment for testing CPT under the previous conditions. Four scenarios for energy-dependent decoherence parameters, ΓEν=Γ×(Eν/GeV)n, n=-1, 0, 1, and 2, are taken into account, and for most of them, DUNE is able to achieve a 5σ discovery potential, having Γ in O(10-23 GeV) for δCP=3π/2. Meanwhile, for δCP=π/2, we reach 3σ for Γ in O(10-24 GeV). © 2019 authors. Published by the American Physical Society.r(s) and the published article's title, journal citation, and DOI. Funded by SCOAP 3 .