  In low energy neutrino factory ($E_{\mu}< 10$GeV) using MIND detector, we
have studied the optimization of $CP$ violation discovery reach in the leptonic
sector for different baselines and different parent muon energy considering
only Standard Model interactions of neutrinos with matter. Considering such
optimized experimental set-up of baseline and energy we have addressed the
question of how $CP$ violation discovery reach could get affected by the
presence of non-standard interactions of neutrinos with matter during the
propagation of neutrinos. For off diagonal NSI elements there could be complex
phases $\phi_{ij}$ which could also lead to $CP$ violation. In presence of
these complex phases we have shown the contours showing the discovery reach of
$\delta$ and $\phi_{ij}$. We have also shown the discovery reach of NSIs in the
same experimental set-up which is optimized for discovery of $CP$ violation in
the leptonic sector.
