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We consider the issue of uniqueness in the estimation of direction of arrival (DOA) and the state of polarization using tripole antenna arrays. An analytical expression for the electromagnetic far-field of the tripole antenna given a certain antenna length and propagation constant is derived and a signal model for the waves received at the antenna array is developed. We show that there are no more than two linearly independent steering vectors for each DOA and that these steering vectors are linearly independent iff they correspond to distinct states of polarization. Furthermore, in the case of a uniform linear array and a one-dimensional DOA parameter space (two-dimensional wave propagation), we use the Haar condition to show that a steering vector is linearly independent of the signal subspace if there are fewer distinct DOAs then there are tripole antennas.