The United States filed an extradition request for the 81-year-old fugitive in January and Polanski has said he doubts it will be honoured.
The dual French-Polish citizen, dressed in a suit and tie, appeared calm and made no comment as he arrived in court alongside his lawyer.
"We are unlikely to have a decision today," Judge Dariusz Mazur said ahead of the hearing, adding it could last "several hours".
A court spokesperson said Polanski and state prosecutors were expected to make presentations.
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Polish prosecutors argue there are legal grounds for the extradition to go ahead, despite a statute of limitations under Polish law on child sex crimes.
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.
The movie will be about France's Dreyfus Affair, the case of an army captain wrongly convicted in 1894 of espionage and treason. His ordeal has become a symbol of injustice and anti-Semitism.
The director of "The Pianist", "Chinatown" and "Rosemary's Baby" was accused of raping Samantha Geimer, who was then 13, after a photo shoot in Los Angeles in 1977 when he was 43.
He pleaded guilty to unlawful sex with a minor, or statutory rape, avoiding a trial, but then fled the country fearing a hefty sentence.
Polanski's lawyers had requested a new hearing to try to close the case on procedural grounds, but a Los Angeles judge refused the move last year.