We report on spectropolarimetric observations of Hα in prominences made with the Télescope Héliographique pour l'Etude du Magnétisme et des Instabilités Solaires and the High Altitude Observatory/Advanced Stokes Polarimeter. Stokes Q and U show the expected profile shape from resonance scattering polarization and the Hanle effect. In contrast, most of the time, Stokes V does not show the antisymmetric profile shape typical of the Zeeman effect but a profile that indicates the presence of strong atomic orientation in the hydrogen levels, to an extent that cannot be explained by invoking the alignment-to-orientation transfer mechanism induced by the prominence magnetic field. We found that the largest signal amplitudes of Stokes V (comparable to that of Stokes Q and U) could be produced by a process of selective absorption of circularly polarized radiation from the photosphere, which requires that the prominence be in the vicinity of an active region. Although recent observations of active region filaments indicate such a selective absorption mechanism as a plausible explanation of the anomalous signals observed, the particular set of conditions that must be met suggest that a different explanation may be required to explain the almost ubiquitous symmetric V signal observed in Hα prominences. Therefore, we speculate that an alternative mechanism inducing strong atomic orientation at the observed level could be due to the presence of electric fields inducing an electric Hanle effect on Hα. Although we are still working toward a careful modeling of this effect, including both electric and magnetic fields, we present some preliminary considerations that seem to support this possibility.