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Polarized light microscopy provides high contrast to birefringent specimen and is widely used as a diagnostic tool in pathology. However, polarization microscopy systems typically operate by analyzing images collected from two or more light paths in different states of polarization, which lead to relatively complex optical designs, high system costs, or experienced technicians being required. Here, we present a deep learning-based holographic polarization microscope that is capable of obtaining quantitative birefringence retardance and orientation information of specimen from a phase-recovered hologram, while only requiring the addition of one polarizer/analyzer pair to an inline lensfree holographic imaging system. Using a deep neural network, the reconstructed holographic images from a single state of polarization can be transformed into images equivalent to those captured using a single-shot computational polarized light microscope (SCPLM). Our analysis shows that a trained deep neural network can extract the birefringence information using both the sample specific morphological features as well as the holographic amplitude and phase distribution. To demonstrate the efficacy of this method, we tested it by imaging various birefringent samples including, for example, monosodium urate and triamcinolone acetonide crystals. Our method achieves similar results to SCPLM both qualitatively and quantitatively, and due to its simpler optical design and significantly larger field-of-view this method has the potential to expand the access to polarization microscopy and its use for medical diagnosis in resource limited settings.