A combination of neutron diffraction, synchrotron X-ray diffraction, and high-resolution extended X-ray absorption fine structure measurements has been used to clarify the correlations between long- and local-range structural distortions across the spin-state transition in powders of LaCoO3 and La0.5Sr0.5Co0.75Nb0.25O3. The analysis of the diffraction data has revealed that the isotropic thermal parameters of Co–O bond abnormally increase below 100 K in both samples, while the temperature dependence of the average Co–O bond lengths is linear from 10 to 300 K. We also have found that the Co–O bond lengths are larger in La0.5Sr0.5Co0.75Nb0.25O3, as compared with the ones in LaCoO3. The X-ray absorption data showed an anomalous decrease of the Co–O bond lengths only for LaCoO3, in contrast to the bond length values obtained by diffraction. The structural anomalies observed by spectroscopy measurements are discussed in terms of the spin-state transition model.