  We present a new search for $H^{0}V$ production, where $H^0$ is a scalar
Higgs boson decaying into $b\bar{b}$ with branching ratio $\beta$, and $V$ is a
$Z^{0}$ boson decaying into $e^{+}e^{-}$, $\mu^{+}\mu^{-}$, or $\nu\bar{\nu}$.
This search is then combined with previous searches for $H^{0}V$ where $V$ is a
$W^{\pm}$ boson or a hadronically decaying $Z^{0}$. The data sample consists of
$106 \pm 4$ pb$^{-1}$ of $p\bar{p}$ collisions at $\sqrt{s}=1.8$ TeV
accumulated by the Collider Detector at Fermilab. Observing no evidence of a
signal, we set 95% Bayesian credibility level upper limits on
$\sigma(p\bar{p}\to H^{0}V)\times\beta$. For $H^0$ masses of 90, 110 and 130
GeV/$c^{2}$, the limits are 7.8, 7.2, and 6.6 pb respectively.
