Two effects induced by the interaction between an electric field E and a permanent electric dipole moment 𝝁𝒆 of a chiral molecule placed in a magnetic field B are discussed as follows: (i) a spin-1/2 nucleus relaxes faster and the increase in the relaxation rate is the same for both enantiomers and (ii) in a two-spin system a cross correlation between the dipole-dipole relaxation mechanism and the interaction between nuclear magnetic shielding and the dipole moment 𝝁𝒆 enables the direct discrimination between the enantiomers. The former effect is too small in magnitude to be observed experimentally. For detection of the latter, an experimental procedure based on the application of an electric field oscillating at a frequency equal to the difference between the spin-precession frequencies of two heteronuclear spins is proposed.