Free on Amazon
She Overheard Murder by Jean Sheldon
http://www.amazon.com/Overheard-Murd...8482927&sr=1-1
On October 29, 1945, Nic Owen made her debut appearance as a radio detective on the new show, 'Inez Ingalls, Private Eye'. Her career began only a few weeks earlier when she was hired to read ad copy and work as an understudy. The murder of the shows star, Carolyn Park, propelled Nic to the lead role and a top spot on the list of suspects. Cecil Park, husband of the murdered woman, wants answers. As does Nora Hahn, Carolyn's 'special friend' for fourteen years.
'She Overheard Murder' introduces characters from the new Nic and Nora Mystery series—mysteries solved by lesbian amateur detectives in post-World War II Chicago.
I haven't read it yet, but it looks interesting to me.