Humidity-sensitive, demand-controlled ventilation systems have been in use for many years in regions with oceanic climates. Some attempts have been made to apply this technology in Poland, which has a continental climate. This article evaluates the performance and energy consumption of such a system when applied in an eight-floor, multiunit, residential building, i.e., the virtual reference building described by the National Energy Conservation Agency (NAPE), Poland. Simulations using the computer program CONTAM were performed for the whole heating season based upon the climate in Warsaw. Besides passive stack ventilation, that served as a reference, two ventilation systems were studied: one standard and one “hybrid” system with additional roof fans. This study confirmed that the application of humidity-sensitive, demand-controlled ventilation in multiunit residential buildings in a continental climate (Dfb) led to significant energy savings (up to 11.64 kWh/m2 of primary energy). However, the operation of the system on higher floors was found to be ineffective. Ensuring consistent operation of the system on all floors required supplementary fans. The introduction of a hybrid mode reduced carbon dioxide concentrations by approximately 32% in the units located in the upper part of the building. The energetic effect in such cases depends strongly on the electricity source. In the case of the national energy grid, savings of primary energy would be relatively low, i.e., 1.07 kWh/m2, but in the case of locally produced renewable energy, the energy savings would be equal to 5.18 kWh/m2.