  We demonstrate that electron electric dipole moment experiments with
molecules in paramagnetic state are sensitive to $P,T$-violating nuclear forces
and other $CP$-violating parameters in the hadronic sector. These experiments,
in particular, measure the coupling constant $C_{SP}$ of the $CP$-odd contact
semileptonic interaction. We establish relations between $C_{SP}$ and different
$CP$-violating hadronic parameters including strength constants of the $CP$-odd
nuclear potentials, $CP$-odd pion-nucleon interactions, quark-chromo EDM and
QCD vacuum angle. These relations allow us to find limits on various $CP$-odd
hadronic parameters.
