  We present a search for associated production of the standard model (SM)
Higgs boson and a $Z$ boson where the $Z$ boson decays to two leptons and the
Higgs decays to a pair of $b$ quarks in $p\bar{p}$ collisions at the Fermilab
Tevatron. We use event probabilities based on SM matrix elements to construct a
likelihood function of the Higgs content of the data sample. In a CDF data
sample corresponding to an integrated luminosity of 2.7 fb$^{-1}$ we see no
evidence of a Higgs boson with a mass between 100 GeV$/c^2$ and 150 GeV$/c^2$.
We set 95% confidence level (C.L.) upper limits on the cross-section for $ZH$
production as a function of the Higgs boson mass $m_H$; the limit is 8.2 times
the SM prediction at $m_H = 115$ GeV$/c^2$.
