Thakur's RTI activist wife Nutan Thakur said CAT issued notice to the Central and state governments asking them to file their detailed counter affidavit within three weeks.
It also issued notice to Gupta to present facts.
The next hearing will be held on September 2.
The UP government had suspended Amitabh Thakur on July 13 and appointed the enquiry officer the next day.
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In his case the charge sheet was issued on July 13 and received by him on July 15 but even before Thakur submitted his reply on July 16, the state government appointed the enquiry officer "in utter violation" of the Rules.
The Uttar Pradesh government suspended Thakur on July 13 within hours of approaching the Union Home Ministry seeking a CBI probe into the rape case slapped against him.
Thakur had stirred a political storm by releasing the text and audio of the conversation purportedly carrying Mulayam's voice.