Polanski, who admitted the offense, fled US justice ahead of sentencing in 1978.
The 82-year old has Polish and French citizenship. Polanski lives in France but has spent time in Poland for a project.
Swiss authorities turned down a US extradition warrant in 2010, after putting Polanski under house arrest.
His current whereabouts are unclear.
Polanski grew up in Poland and is regarded as one of the nation ‘s best living artists, winning an Oscar for The Pianist, which was partly shot in Poland.
His mom died at Auschwitz although film director survived World War Two in the Krakow ghetto.
The BBC’s Adam Easton, in Krakow, says that in the event the court rules in favour of extradition the final decision will soon be taken by the justice minister in Poland.
Polish voters elected a conservative government in the weekend – and officials have said Polanski must be sent to America to face justice.