The construction industry is responsible for large quantities of construction and demolition waste and almost 50% of the worldwide annual resource consumption, putting the environment, its natural resources, and ecosystems under high pressure. Therefore, governments are implementing regional policies that support a circular economy (CE). But how do we know whether these developments will lead to a shift toward a CE on a regional scale? How can we identify hotspots in a value chain and regional economy to support decision-makers and to develop regional policies? We propose an integrated assessment method that considers indicators for environmental impacts and economic benefits by combining Material Flow Analysis (MFA) and Life Cycle Assessment (LCA) with Input-Output Analysis (IOA) as the connecting element. It provides the necessary data and indicators for a holistic and comprehensive evaluation of a region or industry. We demonstrate its benefits and limitations taking the Swiss canton of Aargovia as an example. We analyze which processes in the material flow system of construction minerals are decisive for formulating mass-related or financial policies encouraging a CE. We show that a shift toward a CE can only be captured by combining material and money flows in a joined model, because a significant increase of services—mainly waste management—is a core element in this development. It can only be covered sufficiently by combining environmental and economic assessment. Our model captures the degree to which a regional economy is advanced in the transition toward a CE to compare different regions or analyze scenarios of future developments.