For deck stairs adjacent & parallel to the house wall do I need handrails on both sides?
No, one handrail is required on stairs with 4 or more RISERS. (R311.7.7.) it needs to have a minimum of 1 1/2" clear from the handrail to the wall and shall be mounted not less than 30" nor more than 38" above the nosing of the tread. (R311.7.7.1.) The handrail shall be continuous, but it can be interrupted by newel posts at turns. (R311.7.7.2.) 

The size is complicated, but don't go larger than 2"... (R311.7.7.3.)

AND, all stairs shall be lighted. (R311.7.8.)