Do I have to wear a bottom retainer when I've never had braces on my bottom teeth?

If I treat a patient on one arch only, I always give them retainers for both arches at the end of treatment.  Teeth tend to shift over time and become more crowded (with or without prior orthodontic treatment), so I don't want that to happen to my patient, even if I haven't treated one arch.  
You don't have to wear the retainer on the bottom arch, but if you don't there is a chance that over many years your lower teeth will become more crowded.