We study the capabilities of the DUNE near detector to probe the 3+1 sterile formalism and the non-unitarity of the leptonic sector. We add to the current analyses in the literature, the use of the charged current events for the $\nu_\tau$ appearance channel and the consideration of the energy spectral uncertainty (shape uncertainty) for the different channels which plays an important role, especially at the near detector, and has been usually overlooked in the literature. We find that even with this more conservative and realistic approach, we still obtain an improvement in the sensitivity with respect to the current bounds.