Anthracene-PMDA single crystals display at 2K about 70 meV below a well-known intrinsic charge-transfer exciton three narrow absorption lines, which are attributed to CT excitons bound to defects of a few 10(-5) concentration. All excitons respond very sensitively to electric fields along the molecular stack because of the large dipole moment, about 2 e angstrom, of an ionized donor-acceptor pair, but only intrinsic excitons observe an optical selection rule. Although the triclinic unit cell contains only one pair of molecules, excitons appear in field-modulated spectra as near-degenerate doublets of different parity with very small splitting. The line shape of the EA spectra and selection rules with respect to the polarization of light and orientation of the field are consistent with the inversion symmetry of the lattice and the molecules. The simple crystal structure enables identification of the defects that are responsible for extrinsic excitons. Symmetry consideration based on translation invariance lead to a new interpretation of intrinsic excitons as true crystal states with charge transfer from the donor to the acceptor sublattice.