The question before the jury is: Where was this scene shot?
Despite the "Grand Central" sign, we know it wasn't in New York; Paramount still owned a studio there in Astoria, Queens (where Carole shot a film in 1930), but shifted all of its feature production to Hollywood by 1931. It's possible the scene was done at the studio, although I can't imagine an indoor sound stage where tracks could have been built and rail cars put in. Nor do I believe there was any actual rail link to the studio for freight equipment.
However, there is at least one other very real possibility: it was shot on location in Los Angeles.
What, you say? Yes, L.A. has a subway, but it's only existed since the early '90s, right? Well, yes and no.
For many decades, Los Angeles had a first-rate public transportation system, though it eventually fell out of favor as the automobile culture grew (or was victim to a conspiracy, a theory popularized in the movie "Who Framed Roger Rabbit?", among other places). There were the famed "Red Cars" that took people out to the San Fernando Valley, San Bernardino, Orange County and Long Beach. There were also the less remembered "Yellow Cars," streetcars that served shorter distances throughout the city proper -- and several of these lines terminated at a place called the Subway Terminal Building, at 4th and Hill streets, a block or so north of Pershing Square. The office building, the largest in the city when constructed in 1925, hosted the convergence of these lines at its basement.
The terminal was an integral part of L.A. life, taking people from north and west of the city through a tunnel that was about a mile long to downtown employment. As late as the early fifties, about 100,000 rides went through the terminal, and it was even used as a scene in one episode of the radio version of "Dragnet." But streetcars lost their popularity, gradually replaced by buses, and the terminal was shut down for good in mid-1955, though the building continued to function (and still does).
Over the years, film companies have shot scenes at transit or subway stations, filming either at times when trains weren't operating or on "spur" lines no longer in use by the transit company. It's a practice that continues to this day. It's possible Paramount rented the terminal for a few early-morning hours after the streetcars stopped running, hung a few ersatz New York City props such as the "Grand Central" station sign, painted a few of the cars to vaguely resemble their New York subway brethren, and brought Carole and the other actors and extras there for a quick shoot. (In fact, in an early take, Lombard was knocked down during the scene where she's getting off the train, skinning both knees and bursting the seams of her dress.)
One wonders whether Lombard had any prior experience using the terminal, even before stardom; very little of her acting assignments or related work required trips downtown, or use of mass transit. However, it's possible in her spare time -- particularly in the late 1920s, before she made significant money from acting -- she may have taken streetcars to travel downtown for shopping or to see a movie at one of L.A.'s many film palaces.
Photos inside the terminal are difficult to come by, but here's one I came across of stranded riders at the start of a Los Angeles transit strike in May 1946:
So was the scene actually shot at the Subway Terminal Building? If you know a Los Angeles transit historian, have them get in touch.