Justice Pratibha Rani reserved the verdict after counsel for Ministry of External Affairs (MEA) and accused Rev Joseph Palanivel Jeyapaul concluded their arguments.
Jeyapaul, 59, had approached the High Court after his representation to the Centre challenging the trial court decision recommending his extradition was rejected by the MEA on October 30 and an order to extradite him issued on October 31.
The Centre had told the court that there is a "prima facie" case against Jeyapaul, warranting his extradition.
Jeyapaul was arrested on March 16, 2012 at Chimitahalli near Sathyamangalam in Erode district of Tamil Nadu and has since been lodged in Tihar jail.
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The trial court had said that a "prima facie" a case was made out for Jeyapaul's extradition.
If extradited, he will stand trial on the charge of a "first degree criminal sexual conduct" in Minnesota. If convicted for offences alleged against him there, the accused may get a jail term of up to 30 years.
It had said the girl went to the church in 2004 when he allegedly sexually assaulted her and continued to abuse her till August 2005.