This is the full posterior samples release of the following analyses reported in the paper Tests of General Relativity with GWTC-3 from the LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration: Inspiral-merger-ringdown consistency test (Sec IV B): IGWN-GWTC3-TGR-v1-imr.zip Lorentz invariance violation test (Sec VI): IGWN-GWTC3-TGR-v1-liv.zip Parametrized tests of general relativity (Sec V A): IGWN-GWTC3-TGR-v1-par.zip Ringdown test (Sec VIII A): IGWN-GWTC3-TGR-v1-rin.zip Spin-induced quadrupole moment test (Sec V B): GWN-GWTC3-TGR-v1-sim.zip Each zip file contains HDF5 files that can either be read directly with standard HDF5 tools or using PESummary (https://docs.ligo.org/lscsoft/pesummary/). The curated data set used for producing the figures and table in the paper can be found in https://dcc.ligo.org/LIGO-P2100456/public. If you make use of these data or software in your own work, please include the following acknowledgment. LIGO Laboratory and Advanced LIGO are funded by the United States National Science Foundation (NSF) as well as the Science and Technology Facilities Council (STFC) of the United Kingdom, the Max-Planck-Society (MPS), and the State of Niedersachsen/Germany for support of the construction of Advanced LIGO and construction and operation of the GEO600 detector. Additional support for Advanced LIGO was provided by the Australian Research Council. Virgo is funded, through the European Gravitational Observatory (EGO), by the French Centre National de Recherche Scientifique (CNRS), the Italian Istituto Nazionale di Fisica Nucleare (INFN) and the Dutch Nikhef, with contributions by institutions from Belgium, Germany, Greece, Hungary, Ireland, Japan, Monaco, Poland, Portugal, Spain. The construction and operation of KAGRA are funded by Ministry of Education, Culture, Sports, Science and Technology (MEXT), and Japan Society for the Promotion of Science (JSPS), National Research Foundation (NRF) and Ministry of Science and ICT (MSIT) in Korea, Academia Sinica (AS) and the Ministry of Science and Technology (MoST) in Taiwan. Unless otherwise specified, the contents of this release are licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.