Spatially resolved impedance spectroscopy of a Nafion polyelectrolyte membrane is performed employing a conductive and Pt-coated tip of an atomic force microscope as a point-like contact and electrode. The experiment is conducted by perturbing the system by a rectangular voltage step and measuring the incurred current, followed by Fourier transformation and plotting the impedance against the frequency in a conventional Bode diagram. To test the potential and limitations of this novel method, we present a feasibility study using an identical hydrogen atmosphere at a well-defined relative humidity on both sides of the membrane. It is demonstrated that good quality impedance spectra are obtained in a frequency range of 0.2-1,000 Hz. The extracted polarization curves exhibit a maximum current which cannot be explained by typical diffusion effects. Simulation based on equivalent circuits requires a Nernst element for restricted diffusion in the membrane which suggests that this effect is based on the potential dependence of the electrolyte resistance in the high overpotential region.