His son, Ethan Couch, gained national attention after he escaped jail time in a deadly drunk driving case after a psychologist testified the teen suffered from "affluenza," a condition caused by growing up wealthy.
North Richland Hills police said Frederick Couch, 48, was arrested on a warrant following a traffic stop.
The warrant was issued after police officers responded to a disturbance call last month and said that Frederick Couch, who was not directly involved with the disturbance, told an officer he was a reserve police officer for the Lakeside Police Department.
Police said Frederick Couch offered to show them his "police stuff."
"Frederick Anthony Couch then went back to his vehicle and then took out his wallet. And when it was open, displayed what appeared to be a police badge and an ID suggesting he was a police officer," Investigator Keith Bauman said.
When officers later called the Lakeside Police Department, the department said it had no officer by that name. Investigators then called the state, who told them Frederick Couch was not a licensed police officer in the state of Texas.
"Given the authority that officers are given in the state of Texas and throughout the United States, it is very concerning," Bauman said.
Frederick Couch has a long criminal history, including nearly a dozen traffic citations.
But many remember him for his son, who was found guilty for his role in a drunk driving crash that killed four people, but was only given probation.
Frederick Couch was taken to a detention facility and later released on a $2,500 bond.
Copyright 2014 KTVT via CNN. All rights reserved.
7831 N. Business Park Drive