@bigmac It sounds like you have a trunk mounted bike rack for your car. With some smaller bike frames and step-thru frames, you might need a frame adapter (sometimes also called a top tube adapter), such as the Thule Frame Adapter XT, for the bike to hang properly on your bike rack.
@bigmac Thanks for reaching out!
It can be challenging to get a bike with a sloping top tube, such as the Co-op Cycles CTY 1.1 step through bike, to fit on a trunk mounted bike rack. There are a lot of variables, such as the frame geometry of the bike, the size of the frame of the bike, and width of the bars on the rack, to name a few. Without knowing those details, it is hard for us to make a recommendation on how to make the system work for you. One reviewer of the bike did say it was quite challenging to get the bike on a trunk mounted rack, but it sounded like they were able to make it work. Your best bet may be to head to your local REI store and speak with a rack fitting expert, or you could upload some photos here in the community and we could try to help troubleshoot with you that way. It could be that the frame of your bike or the width of the bars on your rack are not compatible, we'd need to see the system it to help make that determination.
Hopefully this helps, thanks!