Many new physics models can bring in the neutrino oscillation probabilities new sources of CP violation. We investigated how Non-Standard-Interactions and sterile neutrinos in the 3+1 model can modify CP-odd observables like the asymmetries $A_{\alpha\beta} \sim P(\nu_\alpha\to \nu_\beta)-P(\bar{\nu}_\alpha \to \bar{\nu}_\beta)$. Then, we studied the potential of the DUNE experiment to look for hints of new physics measuring only such asymmetries related to different oscillation channels. We showed that if an high energy flux is used, the $A_{\mu e}$ asymmetry could be very useful for this purpose.