The electron spin resonance (ESR) spectrum of CH4+ indicates that some large amplitude tunneling motions among Jahn-Teller distorted structures make the four protons equivalent. A group. theoretical study using the permutation-inversion (PI) group is performed to analyze the hyperfine interaction of the nonrigid CH4+. It is shown that three patterns of the interaction are possible depending upon the type of tunneling motions. Only one of the three patterns is consistent with the experimental spectrum, which is presented in the accompanying paper [J. Chem. Phys. 103, 3377 (1995)].