Tim Riley, p. 127, Tell Me Why, a song by song dissection of the Beatles catalog. He states Paul is the one singing. While the book has some errors (as every single Beatle book does) it is generally a respected and well thought of tome.
This was not what had convinced me tho, I have still been unable to root that out. There is an amazing lack of evidence on this by all of the authors who would normally trot out the info, perhaps because it is assumed everyone already knows. Or perhaps it is assumed that no one really knows. At least one other author (who escapes me at the moment) says it is John.
SO there is less hard evidence and more ambiguity to this then I remembered. So I apologize to all for my hard-assed attitude about it. Although that was prompted by Ydoll's asinine remarks and then set the tone for my defensiveness, the bottom line is I cannot come up with the goods (beyond the above) so it will forever be a take it or leave it proposition.
However consider that Paul had the middle bit, they needed a transition to bring them back to the right key for the last verse, and what they came up with is simple but brilliant. And that Paul is singing about going into a dream and then a dream-like passage follows back into John's bit. It just makes sense, as they only had 4 tracks to play with, that this was him singing as continuing the lyric and his bit and then spliced onto John's final verse. At least to me.