Capacitive sensors have widespread applications in human-machine interaction, Internet of Things, and smart home systems due to their low cost, high sensitivity, and ease of integration. However, improving the sensitivity and sensing distance of capacitive sensors remains a challenging issue. This study proposes a novel capacitive sensor design method based on Kirigami structures, which enhances sensor performance by introducing specific cutting patterns into the conductive layer to leverage edge effects. Through experimental testing and statistical analysis, we systematically investigated the influence of Kirigami geometric parameters on sensor sensitivity and sensing distance. We designed and fabricated 12 different Kirigami structures, including circular flower patterns, array patterns, layered pointed flower patterns, and circular strip structures, and compared them with traditional non-cut structures. The results show that Kirigami structures significantly improved sensor performance. Compared to traditional sensors without Kirigami structures, optimally designed Kirigami capacitive sensors demonstrated approximately a 3-fold increase in sensitivity and up to 170 percent extension in sensing distance. Multivariate regression analysis and nonlinear models revealed complex relationships between Kirigami structural parameters and sensor performance. Notably, the circular strip (three-layer) structure exhibited the best performance, possibly due to its maximization of edge effects and optimization of electric field distribution. This study provides new design insights for developing high-performance capacitive sensors, with potential applications in improving smart home systems and indoor activity monitoring for solitary elderly individuals.