Channel connectivity is an important material property that is considered in making higher-performance proton-exchange membranes. Our group has previously demonstrated that nearly 50% of the aqueous surface domains in Nafion films do not have a connected path to the opposite side of the membrane. These so-called "dead-end" channels lead to a loss in the conductance efficiency of the membrane. Understanding the structure of these dead-end channels is an important step in improving the conductance of the membrane. Although conductive atomic force microscopy is able to provide insight into the connected channels, it does directly report on the dead-end channels. To address this, we use electrostatic force microscopy (EFM) to probe channel connectivity in a Nafion thin film (100-300 nm) under ambient conditions. EFM provided an image of the capacitive phase shift, which is influenced by surface charge, dielectric permittivity, and tip-sample geometry. We studied several individual channels and measured the quadratic dependence of the EFM signal with the bias voltage. Applying a simple parallel plate model allowed us to assign differences in the EFM signal to particular channel shapes: connected cylindrical channels, dead-end cylinder channels, and bottleneck channels.