We present a search for the technicolor particles $\rho_{T}$ and $\pi_{T}$ in the process $p\bar{p} \to \rho_{T} \to W\pi_{T}$ at a center of mass energy of $\sqrt{s}=1.96 \mathrm{TeV}$. The search uses a data sample corresponding to approximately $1.9 \mathrm{fb}^{-1}$ of integrated luminosity accumulated by the CDF II detector at the Fermilab Tevatron. The event signature we consider is $W\to \ell\nu$ and $\pi_{T} \to b\bar{b}, b\bar{c}$ or $b\bar{u}$ depending on the $\pi_{T}$ charge. We sel