The dance is called Girl Hunt Ballet from the 1953 film The Band Wagon directed by Vincente Minnelli. It is around 12 minutes long and is a mini-mystery dance. Fred Astaire plays Rod Reilly, a private detective and he is narrating his story, which is unfolding in the dance. Cyd Charisse plays duel roles as both the innocent blonde and the brunette siren.
Fred Astaire & Cyd Charisse- The Girl Hunt Ballet from The Band Wagon (1953)