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This letter considers the problem of underdetermined estimation of direction-of-arrival (DOA) and polarization parameters, including the degree of polarization (DOP), polarization orientation angle (POA), and polarization ellipticity angle (PEA), for partially polarized (PP) signals with a dual-polarized coprime array. Firstly, the increased dimension due to dual-polarized sensors is reduced by adding two covariance matrices, which facilitates the coarray construction. Then, the holes in the coarray of coprime array are interpolated via utilizing the annihilating relation. At last, the DOAs and array noise variance are obtained by solving an annihilating relation based optimization problem and then used to reconstruct the coherency matrices via the weight least squares (WLS). The polarization parameters can be estimated by performing eigendecomposition on the reconstructed coherency matrices. We show the underdetermined estimation of array noise variance which is difficult for conventional methods is vital for accurate underdetermined estimation of the polarization parameters. The performances of the proposed method are verified by numerical simulations and compared with other representative methods including the Cramer-Rao bound (CRB). [ABSTRACT FROM AUTHOR]