Construction cost and duration are two critical project indicators. It is acknowledged that these two indicators are closely dependent and highly uncertain due to various common factors and limited data for explanatory model calibration. However, the stochastic dependence underlying construction cost and duration is usually ignored and the subsequent probabilistic analysis can be misleading. In response, this study develops a Nataf distribution model of building cost and duration, in which the uncertainties of total cost, unit cost, and duration are respectively quantified by univariate distribution fitting, while their stochastic dependence is inferred by maximum likelihood estimation. This method is applied to the costs and durations of 77 China residential building projects completed between 2011 and 2016. The goodness of fit test illustrates that the data conform well to the developed model. The conditional distributions of cost and duration are then derived and the corresponding conditional expectations and variances are given. The results provide the distribution of building costs for a desired duration and the expected duration given a budget. This, together with the ability to update probabilities when new project information is available, confirms the potential of the proposed model to benefit precontract decision making from a risk perspective.