We present new medium resolution, optical long-slit spectra of a sample of six ultraviolet (UV)/optical and 17 X-ray-selected tidal disruption event candidate host galaxies. We measure emission line ratios from the optical spectra, finding that the large majority of hosts are quiescent galaxies, while those displaying emission lines are generally consistent with star formation dominated environments; only three sources show clear evidence of nuclear activity. We measure bulge velocity dispersions using absorption lines and infer host black hole (BH) masses using the M - σ relation. While the optical and X-ray host BH masses are statistically consistent with coming from the same parent distribution, the optical host distribution has a visible peak near M_BH ˜ 10^6 M_\odot, whereas the X-ray host distribution appears flat in MBH. We find a subset of X-ray-selected candidates that are hosted in galaxies significantly less luminous (Mg ˜ -16) and less massive (stellar mass ˜ 108.5-9 M⊙) than those of optical events. Using statistical tests we find suggestive evidence that, in terms of BH mass, stellar mass, and absolute magnitude, the hard X-ray hosts differ from the UV/optical and soft X-ray samples. Similar to individual studies, we find that the size of the emission region for the soft X-ray sample is much smaller than the optical emission region, consistent with a compact accretion disc. We find that the typical Eddington ratio of the soft X-ray emission is ˜ 0.01, as opposed to the optical events which have LBB ˜ LEdd. The latter seems artificial if the radiation is produced by self-intersection shocks, and instead suggests a connection to the supermassive black hole.