An optically thin gaseous mixture of Κ and low-density He is excited by 570 nm～600 nm of the cw dye laser. The excited K-He molecule is dissociated into the K(4P1/2) or K(4P3/2). The branching ratio is defined as I(D1)/I(D2) where I(D1) and I(D2) are measured intensities of the atomic Κ D1 and D2 lines respectively. The branching ratio is determined in the He density range of (2～8)×10^{23} m^{-3}. The ratio of dissociation rates and the fine structure changing cross section are obtained. The ratio of the dissociation rates approaches 0. 6 as a limit which is independent of the laser frequency.