A titanium dioxide (TiO2) chiral sculptured thin film (STF) fabricated using a serial bi-deposition (SBD) method based on electron beam evaporation has been studied using spectroscopic Mueller matrix ellipsometry (MME). Complete Mueller matrices for the SBD TiO2 chiral STF have been measured using a dual-rotating compensator spectroscopic ellipsometer over the spectral range from 250 to 825 nm in transmission mode, both at normal incidence (θi = 0°) and over a range of oblique angles (5° ⩽ θi ⩽ 60°). A multilayer structurally-graded optical model has been applied to deduce spectra in the three principal indices of refraction that characterize the locally biaxial structure, using as input the complex amplitude transmission ratios deduced from the Mueller matrix measured at normal incidence. A Bragg resonance feature has been observed, and this feature blue-shifts with increasing angle of incidence. Predictions of the transmittance for circularly polarized light normally incident upon the SBD TiO2 chiral STF can be obtained simply by multiplying the unnormalized Mueller matrix by the appropriate Stokes vector, and the results are in excellent agreement with direct measurements.