Charged Higgs Signals in $t\,\overline{t}\,H$ Searches

New scalars from an extended Higgs sector could have weak scale masses and still have escaped detection. In a Type I Two Higgs Doublet Model, for instance, even the charged Higgs can be lighter than the top quark. Because electroweak production of these scalars is modest, the greatest opportunity for their detection might come from rare top decays. For mass hierarchies of the type $m_t>m_{H^\pm}>m_{A^0,\,H^0}$, the natural signal can arise from top quark pair production, followed by the decay chain $t \rightarrow b\,H^+$, $H^+ \rightarrow W^{+(*)} \phi^0$, $\phi^0\rightarrow b\overline{b},\,\tau^+\tau^-$, where $\phi^0=A^0,\,H^0$. These final states largely overlap with those of the Standard Model $t\,\bar{t}\,H^0_{_\text{SM}}$ process, and therefore can potentially contaminate $t\,\bar{t}\,H^0_{_\text{SM}}$ searches. We demonstrate that existing $t\,\bar{t}\,H^0_{_\text{SM}}$ analyses can already probe light extended Higgs sectors, and we derive new constraints from their results. Furthermore, we note that existing excesses in $t\,\bar{t}\,H^0_{_\text{SM}}$ searches can be naturally explained by the contamination of rare top decays to new light Higgses. We discuss how to distinguish this signal from the Standard Model process.