The paper presents the first permanent electric dipole moment d(p) measurements for NaK D-1 Pi state rovibronic levels. Two different methods were applied to obtain d(p) values. Stark effect induced level crossing registered as the changes of fluorescence linear polarization P(E) with external electric field E yielded from one fit both the electric dipole moment value and the Lambda-doubling splitting between e,f substates of an individual rotational state. Another method consisted of obtaining the ratio Delta(ef)(J)/d(p) from E-dependence of the forbidden line appearing in fluorescence as a result of e-f Stark mixing, along with direct Delta(ef)(J) measurement by RF-optical double resonance. The respective dipole moment values obtained are 5.9-6.4 D for the state upsilon’=7, J’=23, as well as 4.5-4.8 D for upsilon’=12, J’=7, the typical errors being ca. 12%-20%. The d(p) value for the latter state reflects d(p) diminution expected due to the admixture of the d(3) Pi state caused by intramolecular interaction. Signal simulation and data fitting have been accomplished using direct Hamiltonian diagonalization accounting for Stark interaction within rotational states J+/-Delta J, Delta J=0,1 and 2 in the initial, excited and final state.