The elastic scattering of electrons with a small intrinsic electric dipole moment (e.d.m.) by spinless targets is discussed in the first and second Born approximations. For large momentum transfer (q ~ 500 Mev/c) the e.d.m. contribution to the elastic scattering cross section becomes important even for values lambda ~10/sup -3/ (where lambda is the e.d.m. in units of e times the Compton wave length of the electron). Thus, it seems likely that experiments involving high-energy electrons may give valuable information on the hypothetical existence and upper limit of the e.d.m. interaction. it is found, in the first Born approximation, that at sufficientiy high energies the existence of the e.d.m. can change the polarization of the electron beam from longitudinal to transverse. Finally, asymmetry effects which appear in the second Born approximation are discussed in detail. Detection of these asymmetries or of the spin correlation effects of the first Born approxi-mation mentioned above would imply the noninvariance of the electromagnetic interactions under parity and time reversal. (auth)