  A line photon incident in an electron-scattering medium is transferred in a
diffusive way both in real space and in frequency space, and the mean number of
scatterings changes as the wavelength shifts from the line center. This leads
to the profile broadening and polarization dependence on the wavelength shift
as a function of the Thomson optical depth $\tau_T$. We find that the
polarization of the Thomson-scattered emission lines has a dip around the line
center when $\tau_T$ does not exceed a few. Various structures such as the
polarization flip are also seen. An application to an ionized halo component
surrounding the broad emission line region in active galactic nuclei is
considered and it is found that the polarization structures may still persist.
Brief discussions on observational implications are given.
