"The judge did not specify the date of the next hearing. He expects to set it for April," court spokeswoman Beata Gorszczyk told reporters after a nine-hour closed door hearing.
The 81-year-old fugitive, dressed in a suit and tie, for his part told reporters he was "tired" at a press conference that began late because he ducked out to take a call from his wife, French actress Emmanuelle Seigner.
"I can also say that the canteen here is good. I recommend it," he added in a bizarre aside.
The United States filed the extradition request in January. Polanski has said he doubts it will be honoured but added that he will comply with the legal proceedings in Poland, where he will begin shooting a new film this year.
"I trust the Polish justice system. I hope everything will go well," he told private Polish television station TVN24 in January.
Polish prosecutors argue there are legal grounds for the extradition to go ahead, despite a statute of limitations on child sex crimes under Polish law.
If the Krakow court clears the extradition, Poland's justice ministry will still have to take the final decision.
The latest extradition bid comes months after the United States tried to have Polanski arrested for sex offences when he travelled to Warsaw for the opening of a Jewish museum in October.
