We have investigated broadband coherent anti-Stokes Raman scattering (CARS) microspectroscopy using the soliton pulses from a photonic crystal fiber. CARS spectrum shows a dispersive shape due to the contributions from a frequency-independent nonresonant component and from a resonant component that corresponds to spontaneous Raman scattering. To extract the resonant component from the CARS spectrum, the functional form of this component was commonly assumed to be a simple Lorentzian function and a nonlinear fitting procedure was used previously. In this study, we derived a CARS spectral function that takes into account the finite spectral width of a pump pulse and the CARS spectrum of diamond powders was fitted using the derived spectral function. It was found that the linewidth obtained using this function agreed with the linewidth of spontaneous Raman scattering much better than the linewidth obtained using a CARS spectral function commonly used previously.