Top quark production offers the unique opportunity to search for a charged Higgs boson ($H^\pm$), as the contribution from $t\to H^+b\to \tau^+\nu b$ can be large in extensions of the Standard Model. We use results from a search for top quark pair production by the Collider Detector at Fermilab (CDF) in the e\tau + \ebar_T+jets and \mu\tau +\ebar_T+jets signatures to set an upper limit on the branching ratio of ${\cal B} (t \to H^{+} b)$ in 106 pb$^{-1}$ of data. The upper limit is in the range 0.5 to 0.6 at 95% C.L. for $H^{+}$ masses in the range 60 to 160 GeV, assuming the branching ratio for {$H^+\to \tau \nu$} is 100% . The $\tau$ lepton is detected through its 1-prong and 3-prong hadronic decays.

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