H$_2$O megamasers residing in the accretion disks of active galactic nuclei (AGN) exhibit Keplerian rotation about the central supermassive black hole (SMBH). Such disk maser systems are excellent tools for diagnosing the kinematic status of the SMBH, and they currently provide the only direct and unambiguous measure of SMBH velocities outside of the Milky Way. We have measured the galaxy recession velocities for a sample of 10 maser disk systems using a combination of spatially resolved HI disk modeling, spatially integrated HI profile fitting, and optical spectral line and continuum fitting. In comparing the SMBH velocities to those of their host galaxies, we find two (out of 10) systems -- J0437+2456 and NGC 6264 -- for which the SMBH and galaxy velocities show a statistically significant ($>$3$sigma$) difference. For NGC 6264 the apparent velocity offset can likely be explained by ionized gas motion within the host galaxy (e.g., from AGN-driven shocks). The velocity measurements for J0437+2456, however, imply a SMBH peculiar velocity of $69.6 pm 12.7$ km s$^{-1}$ (5.5$sigma$). We thus consider J0437+2456 to be a promising candidate for hosting either a recoiling or binary SMBH, though additional observations are necessary to exclude the possibility of a systematic offset between the galactic recession velocity and that measured using the optical spectrum.
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