  We enumerate various effective couplings that contribute to the mixings
between an exotic vector boson $Z^{\prime}$ and the neutral electroweak vector
bosons. The miscellaneous mixing patterns can be evaluated perturbatively. The
effective oblique parameters $S^{\prime}$, $T^{\prime}$, and $U^{\prime}$ are
calculated to compare with the electroweak precision test results. With the
contributions to the non-negligible $U^{\prime}$ parameter from the
$\epsilon_{B,W}$ parameters and the aid of some other parameters to cancel the
negative $T^{\prime}$, the recent CDF $W$-mass anomaly can therefore be
explained.
