High-spin states in $_{35}^{72}\mathrm{Br}_{37}$ were studied using the $^{40}\mathrm{Ca}(^{36}\mathrm{Ar},3pn)$ reaction. The existing level scheme has been significantly modified and extended. Evidence has been found for a spin reassignment of $\ensuremath{-}1\ensuremath{\hbar}$ to the previously observed negative-parity band, which carries implications for the interpretation of a signature inversion in this structure. One signature of the previously assigned positive-parity band is interpreted as negative parity and has been extended to ${I}^{\ensuremath{\pi}}=({22}^{\ensuremath{-}})$ and its signature partner has been observed up to ${I}^{\ensuremath{\pi}}=({19}^{\ensuremath{-}})$ for the first time. The remaining positive-parity band has been extended to ${I}^{\ensuremath{\pi}}=({29}^{+})$. A sequence of states observed to ${I}^{\ensuremath{\pi}}=({22}^{+})$ may be the signature partner of this structure. Configurations have been assigned to each of these three structures through comparisons to cranked Nilsson-Strutinsky calculations.