A new local-topological approach to describe the spatial and angular distributions of polarization parameters of multiply scattered optically anisotropic biological layers of laser fields is considered. A new analytical parameter to describe the local polarization structure of a set of points of coherent object fields, the degree of local depolarization (DLD), is introduced for the first time. The experimental scheme and the technique of measuring coordinate distributions (maps) of DLD The new method of local polarimetry was experimentally tested on histological specimens of biopsy sections of operatively extracted breast tumors. The measured DLD maps were processed using statistical, autocorrelation and scale-sampling approaches. Markers for differential diagnosis of benign (fibroadenoma) and malignant (sarcoma) breast tumors were defined.