The Mysterious Melody AKA Ce soir les souris dansent(1956)

Overview:

An old violin maker has been killed and the investigators have only one clue: on the night of the crime, a blind street musician heard a melody playing in the house. As they do not know the title of the song, they present the music to the famous radio contest known as “The Mysterious Melody”. Little by little the two inspectors will surround the killer after checking that there are several suspects.