The search for the production of the Standard Model Z boson in association with a W boson is motivated and discussed. This is performed using 4.3 fb−1 of Tevatron Run II data collected with the CDF detector in (square root)s = 1.96 TeV proton anti-proton collisions. This is a signature-based analysis where the W boson decays semileptonically into a high-P{sub T} electron or muon plus a neutrino, and where the Z boson decays into two b quark jets (b-jets). We increase the signal-to-background ratio by identifying the b-quarks in the jets with a new neural network-based algorithm. Another neural network then uses kinematic information to distinguish WZ to further increase the signal-to-background ratio. Since our sensitivity is still not enough to achieve an observation, we set a 95% Confidence Level upper limit on the product of the WZ production cross section and its branching fraction to the decay products specified above, and express it as a ratio to the theoretical Standard Model prediction. The resulting limit is 3.9 x SM (3.9 x SM expected).