We study the rotation rates and electric dipole emission of hydrogenated icosahedral fullerenes (single and multishell) in various phases of the interstellar medium. Using the formalism of Draine & Lazarian for the rotational dynamics of these molecules in various astrophysical environments, we find effective rotation rates in the range 1-65 GHz with a trend toward lower rotational frequency as the radius of the molecule increases. Owing to the moderately polar nature of the CH bond, hydrogenated fullerenes (fulleranes) are expected to have a net dipole moment and produce electric dipole radiation. Adopting the same size distribution proposed for fullerenes in the study of the UV extinction bump (2175 Å), we predict the dipole electric emission of mixtures of fulleranes for various levels of hydrogenation. We find that these molecules could be the carriers of the anomalous microwave emission recently detected by Watson et al. in the Perseus molecular complex.