Q:

Reborn in heaven and perfect sila/morality

Does someone have to have perfect morality or sila in order to be reborn in a heavenly realm? If yes, could someone provide the source?

A:

No. A person does not need to have perfect morality to be reborn in a heavenly realm. The quote below should be self-explanatory.
From MN 136:

"Now there is the person who has killed living beings here... has had
  wrong view. And on the dissolution of the body, after death, he
  reappears in a happy destination, in the heavenly world. But (perhaps)
  the good kamma producing his happiness was done by him earlier, or the
  good kamma producing his happiness was done by him later, or right
  view was undertaken and completed by him at the time of his death. And
  that was why, on the dissolution of the body, after death, he
  reappeared in a happy destination, in the heavenly world. But since he
  has killed living beings here... has had wrong view, he will feel the
  result of that here and now, or in his next rebirth, or in some
  subsequent existence.

