Laser percussion drilling is a micromachining process for generating a microhole with a diameter of less than 500 µm. The laser beam heated the material to the vaporization temperature, after which a hole was formed. Laser percussion drilling is increasingly used in micromachining. Monitoring the laser drilling process is crucial for improving the quality of drilling. Among the many methods for monitoring laser drilling, such as optics, sound, and vibration, the method of detecting laser-induced plasma with an external electric field has the advantages of being real time, inexpensive, and free from environmental interference. Therefore, in this study, we used a pair of copper electrode plates to generate a strong electric field around the drilling site to apply a voltage of hundreds of volts. The laser-induced plasma interferes with the electric field and generates electrical signals, which are then measured using an RC circuit. From this measured electrical signal, a waveform was observed for each laser shot. In this study, seven different laser energies were used to test the detected plasma signals and to measure the depth and diameter of each drill hole. We also compared the differences in the detected plasma signals when drilling two different materials (stainless steel SUS 304 and a CoCrMo alloy). The curve fitting method was used to derive a mathematical model of the plasma signal vs the number of laser shots of two different materials. Because the thermal conductivity and ablation rate of different materials are different, the coefficients of the curve-fitting results are also different. The experiments and mathematical models in this study are helpful for understanding the responses of different materials to laser drilling.