Background: Following the Coronavirus Disease 2019 (COVID-19) pandemic, many patients have reported ongoing smell and taste issues. This study aims to investigate the prevalence of olfactory and gustatory dysfunction among patients with a history of COVID-19 and its association with autonomic dysfunction and disability. Patient and Methods: This case–control study included a COVID-19 group (n = 82) and a control group (n = 82). Olfactory dysfunction, including parosmia and taste problems, was explored using self-reports and the Quick Smell Identification Test (QSIT). The association between post-COVID-19 disability severity and taste and smell alterations was also analyzed. Moreover, autonomic function was evaluated using the Composite Autonomic Symptom Scale-31 (COMPASS-31) to assess the association between autonomic and olfactory dysfunction. Results: Significantly higher rates of ongoing smell (26.8%) and taste (14.6%) dysfunction were reported for the post-COVID-19 group compared to the control group. Post-COVID-19 patients reported 36.6 times more smell issues and 8.22 times more taste issues than controls. Parosmia scores were significantly worse in the post-COVID-19 group, while QSIT scores showed no significant difference between the groups. However, those with worse QSIT scores exhibited significantly more ongoing smell issues. No significant association was observed between disability and altered smell or taste. Higher secretomotor dysfunction scores were significantly associated with abnormal QSIT scores and worse parosmia scores; the other domains of the COMPASS-31 scale showed no significant associations. Conclusions: The findings indicated a potential link between autonomic and olfactory dysfunction. Further studies are needed to elucidate the mechanisms underlying persistent olfactory and autonomic dysfunction in post-COVID-19 patients.