Potjaman's secretary is also on trial of lesser charges.
Al Jazeera's correspondent in Bangkok, Selina Downes, says Thailand;s milirtary-installed government hopes that by taking Thaksin's family to court, it can add hard some hard evidence to justify last September's coup.
The army generals had cited alleged corruption in the Thaksin clan as one reason for overthrowing him.
The case centres on allegations that in 1997 - four years before Thaksin came to power - Potjaman transferred shares in the family's telecommunications empire to her brother through her maid's account.
Investigators say it was a deliberate deception to evade tax.
But the family's lawyer says it was a gift from Potjaman to her brother and was therefore tax exempt.
Our correspondent says Thaksin has always credited his wife for what he is today. He says she was instrumental in starting the family's small computer business and developing it into Thailand's biggest telecommunications company, Shin Corp.
The former prime minister is now in exile, but is also facing a string of corruption inquiries.
He could be jailed for up to 15 years if it is found he continued to manage shares he transferred to other people's names - including domestic staff - to evade taxes.
Last year, Thaksin came under fire for selling the family's stake in Shin Corp to Temasek Holdings, the Singapore government's investment company, and structuring the deal to avoid paying capital gains tax.
The controversy drew widespread street protests and the political tension that eventually culminated in last September's coup.