Experimental results for the conditional statistics, such as the velocity conditioned on a conserved scalar and the scalar conditioned on velocity, in a confined liquid-phase rectangular jet are presented and analyzed for a data set collected using simultaneous particle image velocimetry and planar laser-induced fluorescence. The joint velocity-scalar probability density function (PDF) is not joint Gaussian in this flow, as the PDF of the conserved scalar is accurately described by a beta-PDF. The conditional mean velocity is found to agree with a linear model when the scalar is close to its local mean value. A gradient PDF model is found to give poor predictions for the streamwise conditional velocity. However, the improved gradient PDF model predicts both the streamwise and transverse conditional velocities well. A linear model for the scalar fluctuation conditioned on velocity is also tested against the experimental data, showing that this model only obtains good approximations when the joint velocity-scalar PDF approaches a joint Gaussian at farther downstream locations in this flow.