We do indeed have some 2 bike trunk mounted bike rack options for your 2014 CT 200H F Sport that don't require a hitch.
Of the various options, I really like the Thule OutWay # TH45JV. The OutWay uses 2 rubber coated straps to attach to the vehicle, instead of the 6 buckle and nylon strap arrangement used by other racks, allowing you to install and remove the rack in a matter of seconds. This racks comes with a system to lock the rack and the bikes to deter theft.
If you'll be carrying... view full answer...