Speaking in general terms, though, if the numbness is all on one side, it may be a brain problem, such as a stroke, while if the numbness is on both sides, but more prominently in the feet (and possibly in the hands) then it could be a neuropathy. If the numbness is all below one level in the body, then it could be a spine issue, like a herniated disc. Since you describe hands and feet and are talking about your father (who I will assume is an older gentleman, since he has a younger person doing the asking for him), neuropathy may be the most likely. The most common cause of neuropathy in the U.S. is uncontrolled diabetes. Other causes include vitamin deficiencies (B12, B6), inflammation from other diseases, or side effects of medications.
This is not to diagnose - please go to a neurologist for more detailed - and person-specific - responses.
Getting a CT scan can be done as an outpatient, of course, if you speak to your own doctor. If you start feeling more nervous about it, then it warrants a trip to the emergency department.