Hyperfine patterns calculations are carried out for the Na-3 cluster with a view towards understanding the microwave measurements which were performed for three rotational transitions belonging to the ground X electronic state. The calculations take simultaneously into account the pseudorotational motion, the spin-rotation coupling, and the magnetic electron spin-nuclear spin hyperfine coupling. Matching calculated and observed patterns suggests that the cluster is characterized by small pseudorotational tunneling and spin-rotation splittings, some amount of Fermi contact interaction at the two terminal nuclei, and significant dipolar spin-nuclear spin coupling for the central atom.