A non-relativistic theory effective field theory (NREFT) offers a bottom-up framework to classify Dark Matter (DM) - nucleon interactions relevant for scattering at direct detection experiments by organising the interactions in powers of the momentum transfer $ \vec{q} $. This approach generates a number of operators including P-odd and T-odd operators, which require that the relativistic theory generating them have CP violating interactions. We consider the leading order P-odd, T-odd operators viz. $ \mathcal{O}_{10} $, $ \mathcal{O}_{11} $ and $ \mathcal{O}_{12} $ and compare the constraints on these operators from leading direct detection searches and neutron EDM (nEDM). To that end, we perform our analysis using simplified models with charged mediators and compute the loop diagrams contributing to nEDM. We find that constraints on DM scattering cross section from nEDM are several orders of magnitude stronger than the limits from direct searches and the neutrino floor for such NREFT operators for the entire sub-GeV and GeV DM mass range. Our results have interesting implications for prospects of detecting such interactions at direct searches and the NREFT formalism.