We have analyzed here low coherence spectroscopic data by multifractal analysis for obtaining tissue multifratality in depth wise index distribution. Essentially, in this method, a spectral domain interference pattern is recorded in a common path interferometer with a broad band source operated in back scattering mode. The recorded interference spectrum is subjected to Fourier domain processing to compute depth wise index distribution with a resolution of the order of one micron. The experimental set-up was validated, initially, by verifying depths of mica sheet layers and diameter of polystyrene microspheres and later, it was used for assessment of depth wise index (RI) distribution of cervical tissue slices. The structures of cervical tissues at different stages of cancer change rapidly which are manifested in the RI distribution and in turn, are encoded as multi-resolution information. This information can, effectively, be extracted by using multifractal detrended fluctuation analysis (MFDFA), where, multifractal parameters such as Hurst exponent h(q = 2) and width of singularity spectrum (Δα) show definitive change as cancer progresses from grade I to grade II. Moreover, the depth distribution of RI exhibited stronger multifractality (increased Δα) and considerably weakened correlations (decreased h(q = 2)) for tissues with higher pathological grades. Therefore, the technique of low coherence back-scattered (LCBS) interferometry bears a promise of using depth distribution of tissue refractive index and MFDFA analysis appears as a label free biomarker to detect cancer at early.