The CFRP composite materials are widely used in aircraft, automobiles, infrastructures, 3D printing and many more areas where light weight and high strength is a major factor. This study outlines the implementation of Taguchi technique combined with the membership function to optimize the drilling process parameters using Taguchi L27 array with multiple performance characteristics to minimize the objective. The experiments were performed by using three drill bit types at three levels of cutting speeds and feed rates. The responses namely thrust force and torque were measured by using Kistler multicomponent dynamometer 9257B; circularity and cylindricity were measured by using TESA micro-hite 3D Co-ordinated Measuring Machine (CMM). The drilling process parameters which directly influenced the performance characteristics were optimized using response surface methodology (RSM). The ANOVA (Analysis of Variance) results clearly indicated that the feed rate was the significant factor which affected the responses. The experimental values of S/N ratio were compared with predicted values of the membership function, and were found to be in good agreement with each other.