The Bloch equation of the nuclear magnetization of spin-1/2 nuclei in molecules, which have permanent electric dipole moments μe that are placed simultaneously in a magnetic field B and an electric field E, is derived. It is shown that if the principal components of the nuclear magnetic shielding tensor σ and the dipole moment μe are known, then the measurement of the transverse component to the magnetic field B of the nuclear magnetization, which is induced by the application of the electric field oscillating at the half of the spin precession frequency, allows determining the orientation of the dipole moment μe with respect to the principal axis system of the symmetric part of the tensor σ. Four-component relativistic density functional theory computations, which have been performed for several molecules containing heavy nuclei, i.e., 207Pb, 205Tl, 199Hg, 195Pt, and 125Te, indicate that coefficients of the relaxation matrix perturbed by the electric field E are in favorable cases of the order of 1000 pm2 V-2 T-2. Therefore, the spin dynamics is perturbed at experimentally observable levels for the strengths of electric and magnetic fields E = 5 kV/mm and B = 10 T, respectively.