Abstract -- Calculations are performed for the circular polarization of maser radiation from a turbulent, Keplerian disk that is intended to represent the sub-parsec disk at the nucleus of the galaxy NGC4258. The polarization in the calculations is a result of the Zeeman effect in the regime in which the Zeeman splitting is much less than the spectral linebreadth. Plausible configurations for turbulent magnetic and velocity fields in the disk are created by statistical methods. This turbulence, along with the Keplerian velocity gradients and the blending of the three hyperfine components to form the 6₁₆--5₃₂ masing transition of water, are key ingredients in determining the appearance of the polarized spectra that are calculated. These spectra are quite different from the polarized spectra that would be expected for a two-level transition where there is no hyperfine structure. The effect of the hyperfine structure on the polarization is most striking in the calculations for the maser emission that represents the central (or systemic) features of NGC4258. Information about magnetic fields is inferred from observations for polarized maser radiation and bears on the structure of accretion disks.