Ticketed for riding with no hands on the handlebars?

So today I was coming home from school and I got a ticket for having no hands on my handlebars. The cop actually had to run a red light to catch up to me. I was ticketed for having no hands on my handlebars and going "pretty fast". Note that they didn't actually have any sort of radar to see my speed, which I can assure you wasn't over the 35mph speed limit on a single speed casually riding.

I asked the cop if this was a law and where I could read it to which she said to just look at the law book for the city I'm in. After looking at the section that the cop wrote on the ticket, it mentions nothing about proper bike riding technique. I can probably fight this right?

Also I'm mainly posting on here as more of a rant because it happened 20 minutes ago and I'm still pretty pissed about it. It was a $50 ticket as well. Anyone with similar experiences?