More than 90 people, mostly civilians, were killed and nearly 1,900 wounded during the 2010 rallies, which ended in a bloody military operation under then premier Abhisit Vejjajiva, who is now opposition leader.
The demonstrations came after years of political unrest that began months before a 2006 military coup that deposed prime minister Thaksin Shinawatra, long despised by the Bangkok elites but supported by many of the Red Shirts.
Red Shirt supporter Channarong Polsrila was among 16 fatalities identified as likely to have been caused by the security forces' operation, prosecutor Varidsanee Manyawut said.
Channarong was shot dead on a road near Victory Monument in Bangkok at the height of the anti-government protests in May 2010.
"The court will hold an inquest to identify who he was and how he died," Varidsanee told AFP.
Under Thailand's Criminal Procedure Code, prosecutors have the power to submit for inquest any deaths believed related to or involving the authorities, she said.
An initial hearing was held on Monday but examination of 41 witnesses in the case will not begin until mid-June.
Thaksin, who remains a hugely divisive figure, lives overseas to avoid a two-year prison sentence for corruption that he contends was politically motivated.
His sister Yingluck Shinawatra is now prime minister after a resounding election victory last year.