Studying the polarization of paraxial beams propagating through uniaxial anisotropic crystals at an arbitrary angle is a powerful feature to extend the range of utilization of these crystals. In this paper, we derive a general theoretical model, based on the existing theory, to describe the transformations of polarization state in cases of arbitrary beam propagation. Stokes parameters are employed for the determination of polarization state of the light beam. The derived model is applied to a linearly polarized quasi-Gaussian beam propagating through rutile crystal. The dependence of the polarization state of the beam on many parameters such as beam waist, angle of propagation, and thickness of the crystal is investigated. The variation of each of these parameters leads to an extensive and interesting change of the polarization state. Moreover, the results are employed to observe the variations of the spin angular momentum as a function of the above-mentioned parameters. Furthermore, we report on an interesting result regarding the longitudinal component of the propagating field, where we noticed the existence of clearly non negligible values of this component for certain propagation parameters. The results of the current work are promising and can be utilized to obtain the best functioning of the output beam depending on its shape and polarization. In addition, they are promising for other future applications such as designing polarization-based devices which are useful in many fields.