We present photometry, spectra, and spectropolarimetry of supernova (SN) 2012ab, mostly obtained over the course of $sim 300$ days after discovery. SN 2012ab was a Type IIn (SN IIn) event discovered near the nucleus of spiral galaxy 2MASXJ12224762+0536247. While its light curve resembles that of SN 1998S, its spectral evolution does not. We see indications of CSM interaction in the strong intermediate-width emission features, the high luminosity (peak at absolute magnitude $M=-19.5$), and the lack of broad absorption features in the spectrum. The H$alpha$ emission undergoes a peculiar transition. At early times it shows a broad blue emission wing out to $-14{,}000$ km $mathrm{s^{-1}}$ and a truncated red wing. Then at late times ($>$ 100$,$days) it shows a truncated blue wing and a very broad red emission wing out to roughly $+20{,}000$ km $mathrm{s^{-1}}$. This late-time broad red wing probably arises in the reverse shock. Spectra also show an asymmetric intermediate-width H$alpha$ component with stronger emission on the red side at late times. The evolution of the asymmetric profiles requires a density structure in the distant CSM that is highly aspherical. Our spectropolarimetric data also suggest asphericity with a strong continuum polarization of $sim 1-3$% and depolarization in the H$alpha$ line, indicating asphericity in the CSM at a level comparable to that in other SNe IIn. We estimate a mass-loss rate of $dot{M} = 0.050, {rm M}_{odot},mathrm{yr^{-1}}$ for $v_{rm pre} = 100$$,$km$,$$mathrm{s^{-1}}$ extending back at least 75$,$yr prior to the SN. The strong departure from axisymmetry in the CSM of SN 2012ab may suggest that the progenitor was an eccentric binary system undergoing eruptive mass loss.
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