To explore the formation mechanisms of gas phase CH3 OH in cold starless cores, we have conducted high spectral resolution observations toward the cyanopolyyne peak of Taurus Molecular Cloud-1 (TMC-1 CP) with the IRAM 30 m telescope, the Green Bank Telescope, and the Nobeyama 45 m telescope. The spectral lines of CH3OH toward TMC-1 CP are found to have a double-peaked profile separated by 0.5 km/s. Since the double-peaked profile is observed for 13CH3OH, it is not due to optical depth and/or self-absorption effects. The spectral line profile of CH3OH is much different from those of C34S, C3S, and HC7N observed toward this source. The H2densities of the emitting region of CH3OH for the blueshifted and redshifted components are derived to be (1.7±0.5)x104/cm3 and (4.3±1.2)x104/cm3, respectively. These densities are similar to or slightly lower than those found for the other molecules. These results suggest a chemical differentiation between CH3OH and the other molecules, which has indeed been confirmed by mapping observations of the CH3 OH and C34S lines. These results are consistent with the general idea that CH3OH is formed on dust grains and is liberated into the gas phase by non-thermal desorption. The grain-surface origin of CH3OH is further confirmed by the CH3OH/13CH3OH ratio. Weak shocks caused by accreting diffuse gas to the TMC-1 filament, photoevaporation caused by cosmic-ray induced UV radiation, and the desorption of excess reaction energy in the formation of CH3OH on dust grains are discussed for the desorption mechanisms.