RuO₂ is one of the most studied altermagnetic candidate materials. However, it has recently been scrutinized as evidence emerged for its lack of any magnetic order. In this work, we study bilayers of epitaxial RuO₂ and ferromagnetic permalloy (Fe₁₉Ni₈₁) by time-domain terahertz spectroscopy, probing for three mechanisms of laser-induced charge dynamics: the inverse spin Hall effect (ISHE), electrical anisotropic conductivity (EAC), and inverse altermagnetic spin-splitting effect (IASSE). We examine four orientations of RuO₂: (001), (100), (110), and (101). Our results are consistent with charge dynamics induced by only the ISHE and EAC and do not indicate the presence of IASSE for either as-deposited or field-annealed samples, casting further doubt on the existence of altermagnetism in RuO₂. In addition, we find that the combination of ISHE and EAC in the (101) oriented sample produces THz emission that is tunable between linear and elliptical polarization by modulation of the external magnetic field.