Appreciate that safety ground nor earth ground are relevant to eliminating static. Static is a charge difference between any two parts. A ground for that must be one component of the system. Those solid or yellow striped green wires must merge at one part of the entire setup. Any connection to safety (AC receptacle) ground does nothing to discharge static charges.
If static is a problem, then increase humidity to over 40% relative. If static is still created with high humidity, then move on to other reasons for misbehavior.