"All of them are fugitives from justice," prosecutor Khurshid Alam Khan said, adding Sinha was accused of embezzling money and laundering it from one bank account to another.
Sinha headed the South Asian nation's Supreme Court for a landmark verdict on judicial independence that went against the government, but fled Bangladesh in late 2017 amid allegations he had been forced to step aside.
Opposition groups and rights activists said the departure of Sinha, a Hindu, was a blow to the credibility of the judiciary in the Muslim-majority country.
Sinha, 68, now lives in North America.
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He was the first Hindu to be made chief justice of the officially secular Muslim-majority nation of 168 million since its independence from Pakistan in 1971.
Sinha's departure came after a rare statement from the Supreme Court in October 2017 said other judges had accused him of graft and refused to sit with him on the top bench.
Just months earlier, Sinha had led the Supreme Court in a decision that scrapped parliament's power to sack top judges.
The ruling overturned a 2014 constitutional change introduced by authoritarian Prime Minister Sheikh Hasina.
In a written statement issued before he left the country, Sinha expressed dismay over criticism he had faced from the government over the ruling, saying he was "worried about the independence of the judiciary".
He later wrote a book titled "A Broken Dream: Rule of Law, Human Rights & Democracy", detailing the saga, saying he had been forced to resign and flee after being threatened by a military security agency.
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