It was reported that the federal CBI told the judge it needed two weeks to look into the case.
Kumar – dubbed "Doctor Kidney" by the local press – is suspected of luring or forcing hundreds of poor, including many from Nepal, into giving up their kidneys, which he then sold.
Recipients of the organs are said to typically have been wealthy Indians and foreigners for transplants.
The CBI has charged Kumar with grievous hurt with a weapon, wrongful confinement and fraud.
He faced up to a 10 year jail term if found guilty.