Gene Kelly - Singin In The Rain chords

Not sure about the original key but this is how I play it:
[ Tab from: http://www.guitaretab.com/g/gene-kelly/308037.html ]
     C   Am7       Dm7   G
I'm singin' in the rain
Just singin' in the rain
What a glorious feelin'
    Dm     G7
I'm happy again
    Dm7          G7         Dm7     G7 
I'm laughin' at clouds, so dark up above
    Dm7         G7             C          G
The sun's in my heart and I'm ready for love

         C    Am7      Dm7    G
Let the stormy clouds chase
Everyone from the place
Come on with the rain
       Dm           G7
I've a smile on my face
   Dm7           G7          Dm7     G7
I walk down the lane with a happy refrain
      Dm7           G7             C
Just dancinin' and singin' in the rain