  We calculate the effect of the P, CP-odd electron-nucleon interaction on the
electric dipole moment of the $^{199}$Hg atom by evaluating the nuclear spin
matrix elements in terms of the nuclear shell model. It is found that the
neutron spin matrix element of the $^{199}$Hg nucleus is $\langle \Psi |\,
\sigma_{nz} | \Psi \rangle \approx -0.4$ with a dominant configuration of
$p_{1/2}$ orbital neutron. We also derive constraints on the CP phases of
Higgs-doublet models, supersymmetric models, and leptoquark models from the
latest experimental limit $|d_{\rm Hg}| < 7.4 \times 10^{-30}e$ cm.
