  We present a search for technicolor particles decaying into $b\bar b$, $b\bar
c$ or $b\bar u$ and produced in association with $W$ bosons in $p\bar p$
collisions at $\sqrt{s}= 1.96 \mathrm{TeV}$. The search uses approximately $1.9
\mathrm{fb}^{-1}$ of the dataset accumulated in the CDF II detector at the
Fermilab Tevatron. We select events matching the $W$ + 2-jets signature and
require at least one jets to be identified as $b$-quark jets. In the case of
exactly one vertex $b$-tagged events, we apply a neural network flavor
separator to reject contamination from charm and light quark jets. The number
of tagged events and the invariant mass distributions of $W+2$ jets and dijets
are consistent with the Standard Model expectations. We succeed to set a large
95% confidence level excluded region on the $\pi_{T}$ mass v.s. $\rho_{T}$ mass
plane.
