We present the first search for the 5.29 GHz methanimine (CH₂NH) 1₁₀ − 1₁₁ transition toward a sample of galaxy nuclei. We target seven galaxies that host compact obscured nuclei (CONs) with the Karl G. Jansky Very Large Array. These galaxies are characterized by Compton-thick cores. CH₂NH emission is detected toward six CONs. The brightness temperatures measured toward Arp 220 indicate maser emission. Isotropic luminosities of the CH₂NH transition, from all sources where it is detected, exceed 1 L_⊙ and thus may be considered megamasers. We also detect formaldehyde (H₂CO) emission toward three CONs. The isotropic CH₂NH luminosities are weakly correlated with the infrared luminosity of the host galaxy and strongly correlated with OH megamaser luminosities from the same galaxies. Non-local thermodynamic equilibrium radiative transfer models suggest that the maser is pumped by the intense millimeter-to-submillimeter Our study suggests that CH₂NH megamasers are linked to the nuclear processes within 100 pc of the Compton-thick nucleus within CONs.