The PLA and Shanghai local government claim that the Communists liberated Shanghai, but that seems unlikely given their lack of major participation in WW2. I had always heard that the USAAF ferried Nationalist soliders from the southwest of China, and the US Navy landed Marines as well. I'm referring to the liberation from Japanese forces in 1945, not the 'liberation' or communist takeover in 1949.
It was indeed the Nationalist forces which liberated Shanghai on September 10, 1945. I don't really seem to be able to find any more details, but considering the Communists did not hold any major cities in 1945, this seems pretty likely. I'll try to find a better source. Current one is the chronology in "Shanghai: Revolution and Development in an Asian Metropolis".
On another note, I'll have to disagree with you saying the Chinese Communists did not participate in WW2. They did participate, especially in the form of guerilla warfare in the Japanese-occupied parts of Northern China.
And could you maybe find out when the claim that Communists liberated Shanghai was made? The Communist party relaxed/reversed its policy towards mentioning the Nationalist effort in WW2 only relatively recently, around 1980-1990, and even then the Communists were still credited with "leading" the United Front. So it's also possible that the liberation of Shanghai is considered central enough that it couldn't be given up to the Nationalist forces.