A “siren” is a supernatural meremaid-type from Greek mythology. She lured sailors to their doom with her sweet singing.
A Police “siren” is a Gawdawful noisemaker desigened to scare the bejabbers out of you, & get your fat heinie out of the way of the Fuzz when they are in a hurry. On the way to the donut shop, I guess…
How could anybody name one after the other? 
The sirens song is a sign of impending danger. Put that way it makes sense.
Websters: any of a group of female and partly human creatures in Greek mythology that lured mariners to destruction by their singing
Sirens were renowned for their irresistible calls. My guess is that is the origin of the word siren used to describe devices used for calling people in factories etc.
Because “siren” had intermediate meanings, one being:
From this was derived:
So you had the sirens of myth, a musical instrument that had a pretty sound, and finally, a large version of that musical instrument used to give a warning.