In Texas a Helemt not manditory for Adult bicycle riders. But an officer can stop you and check your ID and even your equipment if you present a danger to others or yourself. I had a Park Ranger who stopped me when ridding through our local state park. No biggy, no ticket, and pleasant conversation too, but he said he was going to shake me down every time he saw me ridding without a helmet. So I got one, no problem, but several years latter I took a tumble and certainly would not be writing this if I had not been wearing a helmet... Ha
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