This study develops a coupled cardiovascular-respiratory model that predicts cerebral blood flow velocity (CBFV), arterial blood pressure, end-tidal CO2, and ejection fraction for a patient with congestive heart failure. The model is a lumped parameter model giving rise to a system of ordinary differential equations. We use sensitivity analysis and subset selection to identify a set of model parameters that can be estimated given the patient data. Gradient based nonlinear optimization is used to estimate the subset of parameters. Optimization was caried out first for the cardiovascular submodel and subsequently for the respiratory model. Once a set of optimal parameters were found, the coupled model was computed to confirm that the model is still able to predict the observed data. Results showed that with the approach and methods presented in this paper it is possible to examine and quantify identifiability of model parameters. Using this approach we identified 5 key cardiovascular parameters and 4 key respiratory parameters. Nonlinear optimization techniques was used to estimate these parameters and we tested that values for all parameters were physiologically reasonable for a patient with congestive heart failure.