It is proven that CPT invariance alone requires the electromagnetic structure of a spin-J Majorana particle (J=half interger) to consist at most in toroid multipole moments and distributions with the multipolarity order L=1,2,...,2J; all other usual electric and magnetic multipole characteristics are forbidden. In the spin J=(3/2) case the covariant form of the electromagnetic vertex is obtained in terms of dipole, quadrupole, and octupole toroid form factors. It is suggested that under certain circumstances Majorana fermions with nonvanishing toroid multipole moments might give rise to Cherenkov or transition radiation.