Circular differential transmission in thick films (1.1 mum) of poly{9,9-bis[(3S)-3,7-dimethyloctyl]-2,7-fluorene} is investigated. The vitrified liquid crystalline film obtained after annealing shows high circular differential transmission of light in the wavelength range where the polyfluorene does not absorb (lambda > 450 nm). Using a specifically designed chiroptical setup, we show that circular selective reflection of light in which the circular polarization of the light is retained after reflection, a process which is characteristic for cholesteric liquid crystalline films, makes a negligible contribution to the differential transmission. Using an integrating sphere, we show that circular differential scattering can account for the observed circular differential transmission for lambda > 450 nm.