Metropolitan magistrate Zakir Hossain said another court which deals with internet-related crime would instead hear the bail application, meaning the 31-year-old spinner would remain behind bars on remand at a Dhaka prison.
"The court directed us to move to the cyber court to seek bail. It also asked the jail authorities to look after the health of Sunny as he was sick," Sunny's lawyer M. Muradduzaman told AFP.
Police arrested the left-arm bowler in a Dhaka suburb on Sunday after his longtime girlfriend Nasrin Sultana, 23, filed a complaint two weeks ago.
She also claimed that they had been married since 2014 and filed a separate lawsuit against Sunny on Monday, accusing the player of seeking dowry worth millions from her family.
Sunny has denied all the accusations, including the claim that the couple had been secretly married for more than two years.
If found guilty Sunny could be jailed for up to 14 years and fined 10 million taka (around $125,000) under the country's strict internet law, which local right groups say is being used to crack down on dissent.
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