Investigations of CP violation in the hadron sector may be done using measurements in the ThO molecule. Recent measurements in this molecule improved the limit on the electron electric dipole moment (EDM) by an order of magnitude. Another time-reversal (T) and parity (P)-violating effect in 229ThO is induced by the nuclear magnetic quadrupole moment. We perform nuclear and molecular calculations to express this effect in terms of the strength constants of T, P-odd nuclear forces, neutron EDM, QCD vacuum angle θ, quark EDM, and chromo-EDM.