Search for Higgs Bosons Produced in Association with a Vector Boson in $\mathit{p}\overline{\mathit{p}}$ Collisions at $\surd \mathit{s}=1.8\mathrm{}\mathrm{TeV}$

We search for Higgs bosons produced in association with a massive vector boson in $91\pm 7{\mathrm{pb}}^{-1\mathrm{}}$ of $p\overline{p}$ collisions at $\sqrt{s}=1.8\mathrm{}\mathrm{TeV}$ recorded by the Collider Detector at Fermilab. We assume the Higgs scalar $H^0$ decays to a $b\overline{b}$ pair with branching ratio $\beta$, and we consider the hadronic decays of the vector boson $V$ ( $W$ or $Z$). Observations are consistent with background expectations. We place 95% confidence level upper limits on $\sigma (p\overline{p}\to H^{0}V)\beta$ as a function of the scalar mass $\left(M_{H^0}\right)$ over the range $70<\mathrm{}{M}_{H^0}<140\mathrm{}\mathrm{GeV}{/c}^2$. When combined with an analysis of the case where $V$ is a leptonically decaying $W$, these limits vary from 23 pb at $M_{H^0}=70\mathrm{}\mathrm{GeV}{/c}^2$ to 17 pb at $M_{H^0}=140\mathrm{}\mathrm{GeV}{/c}^2$.