We present a search for charged Higgs bosons in decays of pair-produced top quarks in $p\overline{p}$ collisions at $\sqrt{s}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.8\mathrm{TeV}$ recorded by the D0 detector at the Fermilab Tevatron collider. With no evidence for signal, we exclude most regions of the ( ${M}_{{H}^{\ifmmode\pm\else\textpm\fi{}}},\mathrm{tan}\ensuremath{\beta}$) parameter space where the decay $t\ensuremath{\rightarrow}{\mathrm{H}}^{+}b$ has a branching fraction $>0.36$ and $B({H}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}\ensuremath{\tau}{\ensuremath{\nu}}_{\ensuremath{\tau}})$ is large.