We experimentally investigate capacitance response of a thick ferroelectric GeTe single-crystal flake on the Si/SiO2 substrate, where p-doped Si layer serves as a gate electrode. We confirm by resistance measurements, that for three-dimensional flakes, electron concentration is not sensitive to the gate electric field due to the screening by bulk carriers. Unexpectedly, we observe that sample capacitance C is strongly diminishing for both gate field polarities, so C(Vg) is a maximum near the zero gate voltage. Also, we observe well-developed hysteresis with the gate voltage sweep direction for the experimental C(Vg) curves. From our analysis, the capacitance behavior is explained by the known dependence of the Rashba parameter on the electric field for giant Rashba splitting in GeTe. In this case, the hysteresis in capacitance should be ascribed to polarization evolution in GeTe surface layers, which also allows to realize the regime of dynamic negative capacitance. The latter can be directly observed in time-dependent resistive measurements, as non-monotonic evolution of voltage response to the step-like current pulse. Thus, the negative capacitance regime can indeed improve performance and, therefore, the energy efficiency of electronic devices.