The short-range structure of the neat fluid of fluoroform (CHF3) is investigated around the gas-liquid critical point by measurements of spontaneous Raman spectra of the C-F symmetric stretching (v(2)) and the C-F-3 symmetric deforming (v(3)) modes. The spectra are obtained at reduced temperatures 0.96 less than or equal to T-r = T/T-c less than or equal to 1.06, the conditions of which permit isothermal studies in the gas, liquid, and supercritical states as functions of pressure and/or density. As the density increases, the spectral peaks shift toward the lower energy side and spectral widths become broader. In the supercritical region, the amount of shifting shows nonlinear density dependence, while the width becomes anomalously large. We analyze these density dependences along vibrational coordinates by the perturbed hard-sphere model. The amount of shifting is decomposed into attractive and repulsive components, and the changes of attractive and repulsive energies are evaluated as functions of density and packing fraction, both of which are continuously varied by a factor of 50. For both vibrational modes, the spectral shift consists principally of the attractive component at all densities and temperatures. Here we evaluate local density enhancement as a function of bulk density by the use of the values of attractive shift and by the use of dielectric analysis. Local density enhancement is highest at the bulk density, where the spectral width becomes anomolously broad. We analyze the density dependences of widths by comparing the experimental values with calculated homogeneous and inhomogeneous widths. The experimental results agree with the theoretical calculations. It is elucidated that the main contribution to width is density inhomogeneity. By comparing short-range structure studied in the present study with long-range structure previously studied by small-angle X-ray scattering, we found that the vibrational motion becomes significantly affected by the dielectric structure as the correlation length of the density fluctuation grows longer than the size of a first solvent shell of CHF3. Under that situation, the v(2) mode is more sensitive than the v(3) mode to the dielectric structure in the vicinity of a vibrating molecule.