State-resolved two-pulse correlation measurement is useful to study the time scale and mechanism of photo-induced desorption as well as electronic structures of admolecules before desorption. In photodesorption of nitric oxide molecules from Pt(111) at 250 K induced by 80 fs, 620 nm laser pulses, the yields and translational temperatures reached a maximum at zero delay time. In contrast, the rotational temperature of Ω=3/2 molecules reached a maximum at a delay time of +/-1 ps, while that of Ω=1/2 molecules was enhanced at around zero delay. In addition, the ratio of total yields of Ω=1/2 molecules to that of Ω=3/2 molecules increased at short delay times. All of these results can be explained by the model of rotational heating, including spin-orbit (SO) coupling, where the difference in the correlation time was found to be due to the SO structure in the adsorbed phase.