Kalola,
You can if you want to, but it's not generally necessary. Here's a picture of a 3 prong configuration with a ground strap...
That green wire with the yellow stripe is a ground and it is most definitely connected to the cabinet somewhere. So it will serve as the ground strap (in the above picture).
Here's the thing... say you were going from a 3 prong to a 4 prong. That is, the dryer was originally "designed" for a 3 prong. This means you'd have to "retrofit" it a bit. Take a look at this pic... ( I made this for someone else, so please disregard my somewhat hostile remarks, OK?)
The ground strap has been removed and has been replaced by the ground to the frame. Yours probably does NOT have a ground strap, though... yours uses that Green/Yellow wire for frame ground.
All of that to say this. Don't lose sleep over it. Ya done good.
SG
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