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 often 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 current bounds.