Gotta Dance... Ethel Merman?

Signin In The Rain is the movie. But Gene Kelly signs it in that movie and he's a man (And an amazing talent if I might add.). Debie Rynollds co-stars in it with him but dosen't sing it so I'm not sure what female artist you'd be thinking of. If you like old musicals though, Singing In The Rain is great. The number you're talking about is one of the best parts of the movie. I'm sure that song has been coverd by many talented vocalists of that time era.