The individual lifetimes of three low-lying states in the proton-decaying well-deformed rotational band in the second minimum of the $N=Z$ nucleus ${}^{58}\mathrm{Cu}$ were determined. Doppler-shift attenuated $\ensuremath{\gamma}$-ray lineshapes were analyzed following the fusion-evaporation reaction ${}^{40}\mathrm{Ca}{(}^{24}\mathrm{Mg},1\ensuremath{\alpha}{1p1n)}^{58}\mathrm{Cu}$ and using the EUROBALL \ensuremath{\gamma}-ray spectrometer coupled to ancillary detector systems. The deduced transitional quadrupole moments confirm the predicted increase of deformation towards the bottom of the band. The \ensuremath{\gamma} decay-out strength hints towards a nonstatistical pattern.