Vocal score

You'd probably be able to find sheet music for the Kalmar/Ruby numbers used in the film if you really did some digging. They are a largely forgotten songwriting team from a bygone era, so most of their music is probably sadly out of print. Antique shops might be a good source to find their music. You might check EBay or Amazon or Barnes & Noble, but I doubt you'll have much success there; however, it's better to leave no stone unturned in a case like this. I would say that it would probably be very difficult to get an actual vocal score with the arrangements used in the film itself, as MGM probably didn't publish one. That's just an assumption on my part though. You could also try New York or Los Angeles businesses that deal in sheet music. They are the "entertainment" cities, so things of this nature would be more likely to be there than any place else. Probably sounds a little discouraging, but I hope maybe you'll get some leads from this.