The normal US point of view is that "Jewish" is a religion, not an ethnicity, hence is a choice.
That point of view is not universally shared, of course.
A cursory search tells me nothing of much use.
Apropos of nothing, I found a Pew poll[0] that says... 21% of atheists believe in a god? Huh?
[0] - http://religions.pewforum.org/pdf/report2religious-landscape... ("Conception of God")
And again, if you talk to people who self-identify as "Jewish", you get a rather more complex picture.
The normal US point of view is that "Jewish" is a religion, not an ethnicity, hence is a choice.
That point of view is not universally shared, of course.