In this letter, we report on accurate comparative measurements of Raman scattering from bulk crystalline Si and from hydrogenated amorphous Si thin films before and after their pulse laser annealing, performed for the purpose of Si crystalline grain formation. Being accompanied by the respective optical transmittance/reflectance measurements, these data allowed us to estimate the integrated Raman scattering cross section ratios of crystalline and microcrystalline Si to hydrogenated amorphous Si and to compare the results with those known from the literature. For crystalline Si, the obtained ratio is equal to 0.75, while for microcrystalline Si, it is equal to at least 2. Our results are found to contradict the proposed earlier exponential decay dependence of the integrated Raman scattering cross section ratio of microcrystalline to amorphous Si on the crystalline grain size. The physical reasons, which support our findings, are discussed.