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Both the Wilkinson Microwave Anisotropy Probe (WMAP) and Planck observationsreported the hemispherical asymmetry of the cosmic microwave background (CMB)temperature fluctuation. The hemispherical asymmetry might be stemmed from theprimordial statistical anisotropy during the inflationary era of the universe.In this paper, we study possible implications of the primordial power spectrawith dipolar anisotropy on the CMB temperature fluctuation and polarizations.We explicitly show that the statistical dipolar anisotropy may induce theoff-diagonal ($\ell'\neq\ell$) $TT$, $EE$, $BB$, and $TE$ correlations, aswell as the diagonal ($\ell'=\ell$) $TB$ and $EB$ spectra. In particular,these correlation coefficients are expected to be $m$-dependent generically.These signals of statistical anisotropy might be tested by CMB observations infuture.

Implications of primordial power spectra with statistical anisotropy on CMB temperature fluctuation and polarizations