Mathematical models are widely used to provide evidence to inform policies for tuberculosis (TB) control. These models contain many sources of input uncertainty including the choice of model structure, parameter values and input data. Quantifying the role of these different sources of input uncertainty on the model outputs is important for understanding model dynamics and improving evidence for policy making. In this paper, we applied the Sobol sensitivity analysis method to a TB transmission model used to simulate the effects of a hypothetical population-wide screening strategy. We demonstrated how the method can be used to quantify the importance of both model parameters and model structure and how the analysis can be conducted on groups of inputs. Uncertainty in the model outputs was dominated by uncertainty in the intervention parameters. The important inputs were context dependent, depending on the setting, time horizon and outcome measure considered. In particular, the choice of model structure had an increasing effect on output uncertainty in high TB incidence settings. Grouping inputs identified the same influential inputs. Wider use of the Sobol method could inform ongoing development of infectious disease models and improve the use of modelling evidence in decision making.