Covert communication conceals wireless transmission activity, but conventional multi-antenna designs rely mainly on spatial beamforming and can be constrained by limited spatial degrees of freedom. This paper investigates polarization-reconfigurable antenna (PRA)-aided multiple-input multiple-output (MIMO) covert communication, where Alice and Bob perform transmit and receive polarforming, respectively, and Willie uses a vertically polarized antenna for radiometric detection. We jointly optimize the transmit covariance matrix and the transmit and receive phase shift vectors to maximize Bob's achievable rate under the covertness and transmit power constraints. Under Gaussian signaling, perfect polarized channel state information, and known noise power at Willie, we derive his optimal radiometric threshold and exact minimum detection error probability (DEP) for a finite observation length, and convert the DEP requirement into a deterministic constraint on his received signal power. We further prove that, for a fixed transmission design, positive signal leakage becomes detectable as the observation length tends to infinity. To solve the design problem for a finite observation length, we develop an alternating optimization (AO) algorithm with a generalized water-filling covariance update and closed-form phase updates. Numerical results validate the exact DEP analysis and the rapid convergence of the proposed algorithm. Compared with the sufficient divergence-based condition, the exact covertness constraint permits a $0.99$--$1.12$~dB higher received signal-to-noise ratio (SNR) at Willie, while joint transmit and receive polarforming provides a rate gain of up to $53.8\%$ over the considered benchmark schemes.

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