Despite extensive protective measures, SARS-CoV-2 widely circulates within healthcare facilities, posing a significant risk to both patients and healthcare workers. Several control strategies have been proposed; however, the global efficacy of local measures implemented at the ward level may depend on hospital-level organizational factors. We aimed at better understanding the role of between-ward interactions on nosocomial outbreaks and their control in a multi-ward psychiatric hospital in Western France. We built a stochastic compartmental transmission model of SARS-CoV-2 in the 24-wards hospital, accounting for the various infection states among patients and staff, and between-ward connections resulting from staff sharing. We first evaluated the potential of hospital-wide diffusion of local outbreaks, depending on the ward they started in. We then assessed control strategies, including a screening area upon patient admission, an isolation ward for COVID-19 positive patients and changes in staff schedules to limit between-ward mixing. Much larger and more frequent outbreaks occurred when the index case originated in one of the most connected wards with up to four times more transmissions when compared to the more isolated ones. The number of wards where infection spreads was brought down by up to 53 % after reducing staff sharing. Finally, we found that setting up an isolation ward reduced the number of transmissions by up to 70 %, while adding a screening area before admission seemed ineffective.