Multiresolution analysis on the spatial refractive index inhomogeneities in the epithelium and connective tissue regions of a human cervix reveals a clear signature of multifractality. Importantly, the derived multifractal parameters, namely, the generalized Hurst exponent and the width of the singularity spectrum, derived via multifractal detrended fluctuation analysis, shows interesting differences between tissues having different grades of precancers. The refractive-index fluctuations are found to be more anticorrelated, and the strength of multifractality is observed to be considerably stronger in the higher grades of precancers. These observations on the multifractal nature of tissue refractive-index variations may prove to be valuable for developing light-scattering approaches for noninvasive diagnosis of precancer and early-stage cancer.