Parallel-connected lithium-ion cells are extensively applied in electric vehicles to satisfy the capacity and power capability. However, unavoidable cell-to-cell parameter variations lead to inhomogeneous current and state-of-charge distributions, causing early degradation of the cells. Therefore, knowledge of correlations of the parameter variations on current and state-of-charge distributions is crucial for improving these inhomogeneities. In order to clearly analyze the correlations, this paper provides a simplified analytical circuit model consisting of a resistance and a capacitance in series, and the capacitance is a function of capacity and open circuit voltage slope. Using the two parallel-connected cells analytical model, the current and state-of-charge distributions are theoretically investigated by varying cell parameters. For a large number of parallel-connected cells with Gaussian distributed parameters, a Laplace transform-based approximate analytical model is proposed based on the simplified analytical circuit model and validated by the simulation. Then the model is utilized to deduce mathematical correlations of the standard deviation and mean value of the cell parameters on maximum differences of current rate and state-of-charge. Results verify that decreasing the deviation of the product of cell resistance and capacity can effectively reduce the inhomogeneities, which is helpful for optimal screening approach for parallel-connected new and retired batteries.