There is a need for a good quality p-type accumulation-mode thin film transistor (TFT) using a metal oxide semiconducting channel. P-type cuprous oxide (Cu₂O) has been proposed as a suitable semiconductor, but such TFTs have suffered from unacceptably high off-state currents. This paper studies the main origin of this high off-state current. Capacitance-voltage (C-V) characteristics reveal the accumulation of minority carriers (electrons) in the off-state regime (i.e. for a positive gate voltage). The activation energy extracted from the temperature dependence of the drain current as a function of gate voltage shows an abrupt lowering of the activation energy and pinning of the Fermi energy in the off-state region, which is attributed to subgap states at 0.38 eV from the conduction band minimum. This suggests that an electron flow in the off-state causes the high off-state current in p-type Cu₂O TFTs and not an inability to deplete the channel of holes.