LO phonon-overdamped plasmon coupled modes in n-type epitaxial films of β-SiC have been measured in the carrier concentration range from 6.9×1016 to 2×1018 cm-3. The carrier concentrations and damping constants are determined by line-shape fitting of the coupled modes and compared with the values derived from Hall measurements. The concentrations obtained from the two methods agree fairly well. The Faust-Henry coefficient determined from the fitting is 0.35. The line-shape analysis of the coupled mode has shown that the dominant scattering mechanisms in β-SiC are deformation-potential and electro-optic mechanisms.