Objective of the Study: This cross-sectional study examined the perceived psychological well-being of administrative/technical employees and researchers/lecturers at the University of L’Aquila (Italy) during the COVID-19 pandemic. The study was carried out in two different periods of 2022: April 2022, when remote working was still mandatory, and December 2022, when the pandemic emergency had ended and, in Italy, remote working had become voluntary for two days a week and exclusively for administrative staff. Materials and Methods: Perceived psychological well-being was investigated using the GHQ-12 (Global Health Questionnaire, short-form with 12 items), a self-administered questionnaire created on Google Forms and sent via email to all the employees of the University of L’Aquila. Statistical analysis was conducted using means, standard deviations, and frequency tables for the descriptive analysis of socio-demographic data, while the t-test or Wilcoxon test and the Χ2 test were used to verify the statistical difference and association between categorical variables. Results: Overall, 365 employees, including 118 administrative/technical and 247 research/teaching staff, participated in the survey in April 2022 when remote working was mandatory. Among them, 219 (52.8%) were female and 196 (47.2%) were male. In December 2022, 266 employees engaged in voluntary remote working, including 184 (69.2%) women and 82 (30.8%) men, took part in the study. The most represented age group was 50–59 years old (36.3% of study participants). During mandatory remote working, 83.4% of lecturers reported a perceived level of psychological distress ranging from moderate to severe versus 69.5% of technicians. The percentage of self-reported psychological distress was higher among the technicians forced to work from home (n. 118–42.9%) vs. the technicians working from home on a voluntary basis (n. 157–57.1%), with GHQ score being >14 in 65.5% of enforced remote workers vs. 62.3% of voluntary remote workers. During mandatory remote working, there was a significant difference in the GHQ-12 score between administrative and research staff, particularly related to items such as loss of self-confidence, emotional pressures, and diminished productivity. Moreover, from the comparison between the group of administrative staff engaged in mandatory remote working and those in voluntary remote working for specific GHQ-12 items, a statistically significant difference emerged concerning the perception of not being able to overcome difficulties; the GHQ-12 score was higher in the first group. Significant differences in the overall GHQ-12 score were evident between male and female lecturers, as the latter reported higher levels of perceived stress during mandatory remote working. Discussion: The results confirm that remote working could be associated with a better psychological state of administrative university staff, especially in the case of voluntary remote working. During mandatory remote working, a difference was observed between teaching and administrative staff, with higher stress in the first group and among women. Therefore, our sample appears fragmented in the self-assessment of psychological well-being during remote working, possibly due to profound differences in the organization of work activities between lecturers and administrative employees. Additionally, the increased perception of stress by female lecturers compared to males may reflect gender disparities, as women working from home during the pandemic experienced an increased workload including domestic activities. Conclusions: Remote working is a type of working that has both advantages and disadvantages. An advantage is undoubtedly a better work–life balance; however, the risks of technostress, workaholism, increased sedentary behaviour, and social isolation are negative aspects. This study provides an indicative overview of the psychological state related to remote working in a university setting during the SARS-CoV-2 pandemic. The study might therefore serve as a starting point for further research on the impact of remote working on self-reported psychological well-being, especially in the university environment.