  We derive indirect limits on the charm and bottom quark electric dipole
moments (EDMs) from paramagnetic AMO and neutron EDM experiments. The charm and
bottom quark EDMs generate $CP$-odd photon-gluon operators and light quark EDMs
at the $c$- and $b$-quark mass thresholds. These $CP$-odd operators induce the
$CP$-odd semi-leptonic operator $C_S$ and the neutron EDM below the QCD scale
that are probed by the paramagnetic and neutron EDM experiments, respectively.
The bound from $C_S$ is $\vert d_c \vert < 1.3\times 10^{-20}\,e\,\mathrm{cm}$
for the charm quark and $\vert d_b \vert < 7.6\times 10^{-19}\,e\,\mathrm{cm}$
for the bottom quark, with its uncertainty estimated as 10%. The neutron EDM
provides a stronger bound, $\vert d_c \vert < 6\times 10^{-22}\,e\,\mathrm{cm}$
and $\vert d_b \vert < 2\times 10^{-20}\,e\,\mathrm{cm}$, though with a larger
hadronic uncertainty.
