Not sure about the original key but this is how I play it:

     C5   A5       D5   G5
I'm singin' in the rain
Just singin' in the rain
What a glorious feelin'
    D5     G5
I'm happy again
    D5          G5         D5     G5 
I'm laughin' at clouds, so dark up above
    D5         G5             C5          G5
The sun's in my heart and I'm ready for love

         C5    A5      D5    G5
Let the stormy clouds chase
Everyone from the place
Come on with the rain
       D5           G5
I've a smile on my face
   D5           G5          D5     G5
I walk down the lane with a happy refrain
      D5           G5             C5
Just dancinin' and singin' in the rain