I feel that this is probably a silly question and the answer should be apparent from looking at them but....

I'm looking at racks for carrying bikes on the back of cars and I don't understand how my bike would be attached. I understand how it works for bikes with a cross bar but my bike is a women's bike with no crossbar -it's the same shape as the one in this picture: http://www.breezerbikes.com/im/bikes/uptown-u.jpg

Do you need to get a specific type of rack to ensure women's bikes fit on them or how do they attach?