In 2011, a no-insulation (NI) winding technique was first proposed. Rare-Earth Barium Copper Oxide (REBCO) pancake coils using the NI winding technique are promising to generate an ultrahigh magnetic field, because the NI winding technique drastically enhances the thermal stability. When a local hot spot appears on a turn of the NI REBCO pancake coil, the enforced current can bypass into the adjacent turns to suppress the Joule heat generation. Recently, different types of REBCO coils to enhance the thermal stability by escaping the current flow from a local hot spot have been researched and developed. A few years ago, a REBCO single pancake coil whose upper surface was coated with conductive epoxy resin was proposed as one kind of NI winding techniques. The high thermal stability of conductive-epoxy-resin-coated (CERC) REBCO single pancake coil was demonstrated through an overcurrent test. However, the current behavior in the coil is still unclear. Therefore, we have newly developed an equivalent circuit model for CERC REBCO pancake coils. The sudden discharging and overcurrent tests were simulated for CERC REBCO pancake coils, and the resistance parameters were varied to investigate the coil stability. Index Terms-Conductive-epoxy-resin-coated REBCO coil, magnet stability, no-insulation winding technique, quench protection.