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The video descriptor says "1930s" but as one observant YouTube commenter writes:
This ISN'T 30's…this is 1942 at the earliest (but I'd say most likely mid to late 40's), because Red Skeleton's prints weren't made outside the Chinese Theatre until June 18th 1942 (it says the date RIGHT THERE). Rex Harrison also wasn't a star in Hollywood until the mid 40's (his first US movie wasn't until 1946) And the cars look like mid 40's style