Texas law saws something similar.

Now, one could argue that the bike is equipped with a rider, and the rider is able to make the braked wheels skid, or that the pedals are the brake, and by using the pedals the operator can make the braked wheels skid ... but I don't know how effective such arguments have been. Certainly, the police do occasionally give "no brake" tickets to riders of bicycles without brakes, and usually the cyclists just pay them (rather than trying to right them.)

Note that the way this law is written is sort of unfortunate, as most upright bicycles cannot skid the front wheels, no matter how good the brakes are -- instead the bike will endo before the front wheel skids. So reading this law literally (as laws should be read), any bike with a front brake (either only a front brake or both a front and back brake) violates the law. That said, I've never heard of anybody getting a ticket for it, so it's probably OK.