The film director has been wanted by US police since 1977 after fleeing the country before he could be sentenced for assaulting a 13-year-old girl.
US authorities contacted Polish officials as Roman Polanski attended the opening of a Jewish museum in Warsaw.
Roman Polanski was questioned in Krakow.
“Roman Polanski said he would comply with all requests made by prosecutors in this case and provided his address,” Police justice ministry spokesman Mateusz Martyniuk told AFP.
“Prosecutors therefore decided not to arrest him in connection with a possible US extradition request.”
The Polish government confirmed that the US had contacted authorities asking them to arrest Polanski after he travelled to Warsaw for the opening of the Museum of the History of Polish Jews.
Mateusz Martyniuk said Roman Polanski’s extradition was still possible, but as the US had not yet forwarded an extradition request, Polanski “is a free citizen and is free to travel”.
He was held in Switzerland in 2009 after travelling to Zurich to pick up a prize at a film festival.
However, the extradition bid failed and he was eventually allowed to return to France.
He has been to Poland several times in recent years and was pictured on television at the opening of the Museum of the History of Polish Jews.
In 2010, the Polish prosecutor general said Roman Polanski could not be extradited because under Polish law too much time had passed since the offences.
Police in Los Angeles charged the director with s** offences including rape in 1977 before he accepted a plea deal, but he fled the country on the eve of his sentencing.
Last year his victim, Samantha Geimer, now 51, published her account of what happened in a book called The Girl: A Life Lived in the Shadow of Roman Polanski.
Roman Polanski is currently directing a stage show in Paris called The Vampires’ Ball, but has said he wants to shoot a film on location in Poland on the condition he will not face extradition.
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