In this paper, we propose local C-V mapping as a novel method for characterizing ferroelectric domain switching on a nanoscale. This method is an extension of scanning nonlinear dielectric microscopy (SNDM), which is one of the ferroelectric domain observation methods. In the conventional SNDM, a small AC bias is applied to the sample to determine the polarization direction by the phase of the response signal of the capacitance variation induced by the AC bias. On the other hand, in the local C-V mapping proposed this time, a large-Amplitude AC bias is applied to the sample, and the capacitance variation is acquired under the condition that polarization switching occurs. When the sample is a ferroelectric material, the observed C-V curves draw characteristic butterfly-shaped loops. By analyzing these C-V butterfly curves, various information on the domain switching dynamics can be obtained. While conventional C-V measurements are generally performed on a macroscale using micro-to millimeter-scale electrodes, the probe microscopy framework and the high capacitance sensitivity of SNDM enable us to measure local C-V curves with a nanoscale probe tip. In this study, we characterized a randomly-oriented HfO2 film as a demonstration of the proposed method. As a result, we succeeded in visualizing how the switchable and unswitchable regions coexist in the real space. In addition, even inside the switchable region, the observed C-V curve shapes varied depending on the position, suggesting the spatial inhomogeneity in domain switching properties. This method also allows us to map parameters extracted from the C-V curve datasets. Such parameter maps provide a wealth of information on the nanoscale distribution in the switchable polarization, coercive field, and local imprint.