High-resolution spectra, including hyperfine structure, have been observed for numerous vibrational-rotational levels (v,N) of the 4 3 ⌺ ϩ Rydberg state of the NaK molecule. The data have been used to construct a Rydberg-Klein-Rees potential curve, and this molecular potential has been further refined using the inverse perturbation approximation method. Bound-free emission from the 4 3 ⌺ ϩ electronic state to the repulsive a(1) 3 ⌺ ϩ state has also been measured and used to determine both the absolute vibrational numbering and the transition dipole moment function M (R). The experimentally derived potential curve and M (R) are compared with recent theoretical calculations of Magnier et al.; the agreement is very good. Each of the levels (v,N) is typically split into three sets of sublevels by the Fermi contact interaction bI"S. Further splitting ͑of order 0.004 cm Ϫ1) has been attributed to the spin-rotation interaction ␥N"S. The patterns observed exhibit a clear transition from Hund's case b ␤S for small N toward Hund's case b ␤J for large N. The data can be fitted very well using a theoretical model based on setting up and diagonalizing a 12ϫ12 Hamiltonian matrix with two adjustable parameters (b and ␥͒. The values of b that fit the data best are ϳ(0.99 Ϯ0.04)ϫ10 Ϫ2 cm Ϫ1 , with a weak dependence on v. The best fit values of ␥ are in the range 1-6ϫ10 Ϫ4 cm Ϫ1 and depend strongly on v. The values of ␥ appear to exhibit anomalous structure for (v,N) levels perturbed by nearby levels of the 3 3 ⌸ state.