Robin Hood is too early for Shakespeare to have been involved. The first known literary reference was in
Piers Plowman, which was written around 1377.
"I can noughte perfitly fit my pater-noster, as the priest singeth, but I can rymes of Robin Hood and Randolf Earl of Chester, as neither of owre lorde nor of owre lady, the leste that ever was made."
No one knows who first told the story, but the bulk of writings and plays about Robin Hood were written in the 15th century, a century before Shakespeare's birth,
Piers Plowman was another century earlier, and there is good reason to believe the legend was around at least a century prior to that (mid-13th century). There is shakey evidence that suggests that Robin Hood was a real person who lived in the late 12th and early 13th centuries.
here's a bit of info I uncovered.
