The rapidly expanding field of Scan-to-BIM applications highlights the importance of model uncertainty assessment in describing the quality of modeling results. Although there have been recent research advancements in point cloud-based building modeling, there has been limited investigation into accurately analyzing error propagation. This paper estimates the geometry uncertainty in 3D modeling based on a strict application of geodetic stochastic modeling. Statistical uncertainty is incorporated into the building reconstruction process and procedures that enable self-verification within this process are developed. The method can be successfully used to evaluate the dimensional uncertainty of generated BIMs, which is especially important in the field of civil engineering with high accuracy requirements concerning metric quality control. Follow-up research will also consider systematic errors and apply the methods to other 3D point cloud acquisition techniques.