would you vote in a church* if that's where your assigned polling station is located?


*an "evangelical free church," if such distinctions matter.

According to R. Moshe Shternbuch in his Shu"t Teshuvot Ve-hanhagot Volume 2, if it's in something like a social hall as opposed to the sanctuary, it's permitted:

http://smg.photobucket.com/albums/v336/mel...rent=voting.jpg

I have voted in a Presbyterian church in my town on multiple elections, but it was in some kind of general hall not the sanctuary.

Provided that the polling place was not in the chapel, I would have no problems with it.

what if you won't know till you get there?

I have no idea. But I'd be surprised if a church allowed polling in the sanctuary proper. Don't they have their own rules about what's allowed in their sanctuaries and rules about rendering unto Ceasar but not in what they consider sanctified and consecrated?
That said, were the polling to actually be in the sanctuary, I would assume that would be very problematic halachically.

And therefore would it also be very problematic legally?

It would certainly make for a valid case of voter disenfranchisement.