The (39)K(2) 2 (3)Sigma(g) (+) state has been observed by perturbation-facilitated infrared-infrared double resonance spectroscopy and two-photon excitation. Resolved fluorescence spectra into the a (3)Sigma(u) (+) state have been recorded. The observed vibrational levels have been assigned as the v=23-25, 27, 28, 31-33, 38-45, 47, and 53 levels by comparing the observed and calculated spectra of the 2 (3)Sigma(g) (+)-->a (3)Sigma(u) (+) transitions. Molecular constants have been obtained using a global fitting procedure with a comprehensive set of experimental data. Fine and hyperfine splittings have been resolved in the excitation spectra. Perturbations between the 2 (3)Sigma(g) (+) and 2 (3)Pi(g) states were observed. The hyperfine patterns of the 2 (3)Sigma(g) (+) levels are strongly affected by the perturbation. The perturbation-free and weakly perturbed levels follow the case b(betaS) coupling scheme, while the perturbed levels follow case b(beta J) coupling. A Fermi contact constant, b(F)=65+/-10 MHz, has been obtained. Intensity anomalies of rotational lines appeared both in the 2 (3)Sigma(g) (+) approximately 2 (3)Pi(g)<--b (3)Pi(u) excitation spectra and in the 2 (3)Sigma(g) (+) approximately 2 (3)Pi(g)-->a (3)Sigma(u) (+) resolved fluorescence spectra. These intensity anomalies can be explained in terms of a quantum-mechanical interference effect.