When Padme died on Polis Massa, her body was in the possession of Obi-Wan, Yoda and Bail Organa. However, we can assume she was handed over to Imperial management since she was permitted a very public state funeral on Naboo - something the Jedi cannot personally organise at this point in time without attracting Imperial attention.
How did they deliver it to the Empire without arousing suspicion?
Also, what is the official Imperial statement on her cause of death? Since the Empire permitted the state funeral, we can assume that the Emperor did not expose her relationship with the "traitorous" Jedi Anakin Skywalker. The surviving Jedi also covered up the birth of the Skywalker twins by setting up the illusion her child (Anakin nor Palpatine knew there was more than one until Endor) died with her, still in the womb. So it can't be said that she died of a "broken heart" nor in childbirth.
So what did the Empire tell the galaxy?
