The ruling said that Thammanat Prompao, a deputy agriculture minister and power-broker in Prime Minister Prayuth Chan-ocha's ruling coalition, did not violate the constitution because he had not been convicted by a Thai court.
"Although Thammanat received judgement, it was from a court in New South Wales, Australia ... but not a judgement from a Thai court and so is not prohibited from holding office based on constitution," it said in its decision.
Thammanat in 2019 denied wrongdoing and dismissed reports by two newspapers in Australia, the Sydney Morning Herald and the Age, that he had been jailed there for four years on a drugs charge. The newspapers have stood by their stories.
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In its decision on the complaint by 51 opposition politicians, the Thai court said it had requested from parliament and the foreign ministry evidence of the conviction, including Australian court rulings made in 1994 and 1995, which were not forthcoming.
Thammanat has said he had been caught with flour and not heroin. He has, however, admitted to having been convicted of an unspecified minor offence in Australia.
Thammanat was involved in forming the coalition led by Prayuth following an election in 2019 that saw him stay on as premier, five years after he led a military coup against an elected government.
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Opposition parties have said the rules of that election were written to ensure victory for the party of Prayuth, which he rejects.
Prayuth has since consolidated power, helped by the Constitutional Court's disqualification of the opposition Future Forward Party, a decision that triggered months of youth-led protests demanding his resignation and reform of the Thai monarchy.