The effectiveness of energy-efficiency measures in a district-heated building can be complex, as it depends on how energy is produced and used. In this study, a primary energy analysis was conducted based on a case study of a Swedish apartment building that is connected to a district heat production system while considering different climate change mitigation policy instruments including carbon taxes corresponding to Social cost-Business-as-usual or Social cost-550 ppm scenarios. The potential to reduce final heat and electricity demands by different energy-efficiency measures was analyzed for the building used in the case study. The impacts of reducing final energy from the different energy-efficiency measures and the climate change policy instruments on primary energy use and cost of district heat production were investigated using a systems analysis approach. We discussed the importance of analyzing the demand and supply sides and their interaction to minimize primary energy use in district-heated buildings. We showed that climate change mitigation policy instruments have a minimal effect on heat production costs for optimally designed district heat production. The primary energy savings for the energy-efficiency measures depend partly on the characteristics of the district heat production system, which is influenced by the policy instruments.