Local distortions around a Ni dopant in the hole-type La2-xSrxCuO4 superconductor system were studied by x-ray-absorption fine structure (XAFS) using single crystals over a wide hole-doping range. Two distinct interatomic distances between Ni and in-plane oxygen appear in the Ni K-edge extended XAFS. Combined with previous results on hole-localization effects by Ni doping, two types of charge states are strongly indicated for Ni. This duality disqualifies a magnetic-impurity picture for Ni dopant in the superconducting phase of cuprates.