The well-known spherical complex optical potential (SCOP) and complex scattering potential-ionization contribution (CSP-ic) methods with appropriate modifications are applied to the CH3X (X = F, Cl, Br, and I) molecules to compute positron scattering cross sections, which rather is the first theoretical attempt to report the same. Besides, various inelastic cross sections are also predicted for the first time in this Article. We have utilized the multiscattering spherical complex optical potential (MSCOP) approach to derive these cross sections. In general, a reasonable accordance has been found between the present total cross sections and the experimental measurements. Apart from the inconsistency between the present theoretical and previous experimental cross sections in the low energy region, the present theory is found to produce consistent and reliable results at all other energies.