Quantitative fluorescence spectroscopic Mueller matrix measurements from the connective tissue regions of human cervical tissue reveal intriguing fluorescence diattenuation and polarizance effects. Interestingly, the estimated fluorescence linear diattenuation and polarizance parameters were considerably reduced in the precancerous tissues as compared to the normal ones. These polarimetry effects of the autofluorescence were found to originate from anisotropically organized collagen molecular structures present in the connective tissues. Consequently, the reduction of the magnitude of these polarimetric parameters at higher grades of precancer was attributed to the loss of anisotropic organization of collagen, which was also confirmed by control experiments. These results indicate that fluorescence spectral diattenuation and polarizance parameters may serve as potentially useful diagnostic metrics.