As noted earlier in this week's review, the existence of a book entitled "Our Second Murder" is a very strong hint that there must have been a first one. And, indeed, Torrey Chanslor's first book about the Beagle sisters is called just that - "Our First Murder," and it was published in 1940.
In their first case, Amanda and Lutie Beagle (and their cousin and Watson, Marthy) are confronted with a headless corpse discovered in a theatrical boarding house. You might not think that a couple of sisters from a small town in upstate New York, circa 1940, would have a good idea about how to go about solving a murder case in New York City - but you'd be wrong. The Beagles are determined to make a success out of the private detective business they inherited from their older brother. And they do so quite wittily.
I did review this on a Classic Mysteries podcast a couple of years back, and you can listen to the full review here. According to the book's blurb, the New York Times called the book "Delightful," and that would seem to be an admirable description.