If she stood her ground and refused to pay the fine, the nice police officer would handcuff her and put her in jail. Is that when it becomes a police state?
Not true. If she stood her ground, she'd be granted a court date, where a judge (not a police officer) would hear her case. The burden of proof would be on the state, and she would have the right to request a trial in which some number of her peers would render a verdict. If she lost she would have the opportunity to appeal.
Still a police state?