The main aim of the present study was to psychophysically evaluate smell and taste functions in hospitalized COVID-19 patients and to compare those results with a group of healthy subjects. Another aim of the study was to assess the relationship of changes in patients' smell and taste functions with a number of clinical parameters, symptoms, and other physiological signs as well as with severity of disease. Olfactory and gustatory functions were tested in 61 hospitalized patients positive for SARS-CoV-2 infection and in a control group of 54 healthy individuals. Overall, we found a significant impairment of olfactory and gustatory functions in COVID-19 patients compared with the control group. Indeed, about 45% of patients self-reported complaints about or loss of either olfactory or gustatory functions. These results were confirmed by psychophysical testing, which showed a significantly reduced performance in terms of intensity perception and identification ability for both taste and smell functions in COVID-19 patients. Furthermore, gustatory and olfactory impairments tended to be more evident in male patients suffering from more severe respiratory failure (i.e., pneumonia with need of respiratory support need during hospitalization).