In recent years there have been large improvements in constraining the extended Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrix element, $|U_{\tau 4}|^{2}$, which describes the mixing between the active $\nu_{\tau}$ and an additional heavy neutral lepton (HNL). We present a model-independent search for a HNL, capable of mixing with $\nu_{\tau}$ using data from \babar. A total of 424 $fb^{-1}$ of electron-positron data is analyzed. Upper limits at the 95 $\%$ confidence level of $2.31 \times 10^{-2} < |U_{\tau 4}|^{2}< 5.04 \times 10^{-6}$ are set, across the mass range $100 < m_{4} < 1300 ~\text{MeV}/c^{2}$. More stringent limits are being placed at higher masses.