  A non-relativistic effective field theory (NREFT) offers a bottom-up
framework to classify Dark Matter (DM)-nucleon interactions relevant for
scattering at direct detection experiments by organizing the interactions in
powers of the momentum transfer $\vec{q}$ and DM velocity $\vec{v}$. This
approach generates a number of operators including P-odd and T-odd operators;
these can only be generated from a relativistic theory with 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 from
the bound on the neutron EDM (nEDM). We perform our analysis using simplified
models with charged mediators and compute the loop diagrams contributing to the
nEDM. We find that constraints on the DM scattering cross section from the
bound on the nEDM are several orders of magnitude stronger than the limits from
direct searches, and even well below the neutrino floor for such NREFT
operators, for the entire sub-GeV to TeV DM mass range. This indicates that
these operators need not be considered when analyzing data from present or
future direct dark matter detection experiments.
