How can you be arrested just on another person's say so?

Charged with Impersonating a police man because of the cloths he had on and the car he drove. There was no physical contact or property contact. Just verbal between two people, he said she said. There was no threating, Girl pull over two lanes in front of person charged liked to have wrecked two people then she pulled in a convenient store and one of the vehicles pulled in the same parking lot and told her what an idiot she was. She must have gotten bad and call police and told them she thought he was a cop.