Photolysis of a methyl radical CH3 in solid parahydrogen produces a methane molecule CH4 via the reaction between an intermediate singlet methylene (CH2)-C-1 and a parahydrogen molecule H-2. Conservation of nuclear spin during the reaction has been investigated by the intensity distribution of the rotation-vibration spectrum of methane produced by the reaction. It was found that the population of each nuclear spin state of methane just after the reaction was different from that of the statistical ratio, which indicates that a nuclear spin selection rule does exist in the reaction. However, the observed population was significantly different from the theoretically predicted ratio. The discrepancy between the experiment and the theory may indicate a breakdown of the nuclear spin conservation during the reaction, if the reaction mechanism in solid parahydrogen is the same as in the gas phase.