AUSTIN — The Texas Rangers flash the baddest badge in the Lone Star State. They’re the top cops working the biggest crimes beneath iconic white cowboy hats. They’re the bodyguards for the governor.

All of which raises the question: Why are they investigating a Twitter prank poking fun at a small-town city council?

Since at least August, members of the state’s 150-man elite police force are getting to the bottom of who’s behind parody Twitter accounts lampooning council members in what’s arguably the law-and-order headquarters of Texas: Huntsville, home to the nation’s busiest execution chamber.

The mock tweeters include one councilman’s moustache publishing zingers that include, “(Councilman) Keith (Olson) likes to abuse his powers like I like to abuse his face.” Another from the handle Laughable Loll cracked, “I shined my head extra special for tonight so the camera would reflect off of it.”

Walker County District Attorney David Weeks asked the Texas Rangers to investigate whether the tweets may run afoul of harassment laws.

That’s an absurd explanation to one of the tweeters, who called it a waste of taxpayer dollars, and to constitutional experts who say the tweets are a cut-and-dry case of First Amendment rights.

“When I think of the Texas Rangers, I think of people who are committing felonies,” said Katie Newman, who, The Huntsville Item reported Thursday, has admitted to creating one of the fake accounts. “It would strike me as odd that a Texas Ranger would be involved in a parody account of council members in little Huntsville, Texas.”

A spokesman for the Texas Rangers, in a brief statement responding to questions about why it would look into such tweets, said only that the Rangers work with district attorneys who request assistance.

“The amount of time spent on this inquiry is a matter of hours so far,” spokesman Tom Vinger wrote in an email.

It doesn’t even warrant that much time, according to some law experts.

David Anderson, a law professor and First Amendment expert at the University of Texas at Austin, said neither prosecutors nor the Rangers have “any business” investigating tweets if the content is simply parody or satire. He said that even a tweet implying that a council member committed domestic abuse — as one council member claims — would be a libel matter taken up in a civil lawsuit, not in criminal court.

“It’s ridiculous,” Anderson said.

Few badges pack more lore than those of the Texas Rangers. They’ve followed the trail of Bonnie and Clyde, fought the Comanches when Texas still had its sovereignty and snuffed out smugglers during prohibition. Their Wild West legend has inspired characters from the masked “Lone Ranger” to Chuck Norris playing the karate-kicking “Walker, Texas Ranger.”

Today, the Rangers have a lower profile as the state’s lead criminal investigators. When polygamist leader Warren Jeffs built a massive compound for his followers in West Texas, the Rangers were the ones knocking on the doors in the middle of the night in a raid that produced widespread allegations of sexual abuse. A highly secretive “Ranger Recon” team patrols the border with the stated purpose of keeping drugs and cartel violence from Mexico at bay.

Weeks said asking the Rangers to investigate the tweets was appropriate.

“In looking at it, it’s more the idea that you have someone totally uninvolved looking at an issue that may have political ramifications,” Weeks said. “I try to err on the side of caution in those cases.”

Twitter is swarming with the fake doppelgangers of celebrities and politicians. Chicago Mayor Rahm Emmanuel still has fewer followers than a well-known parody account that stopped tweeting a year ago, while Not Bill Walton exaggerates the eccentricities of the former basketball star to an audience of 125,000 followers. The tone of fake accounts range from gentle caricatures to the mean-spirited.

The mock accounts in Huntsville sprang up last year, most for months had had only a few dozen followers and the most popular, Phony Don Johnson and Fake Keith Olson, now have more than 100 followers each.

 Newman, who unsuccessfully ran for a council seat last year, said a Ranger in August interviewed her for more than an hour at his office in Huntsville.

Newman said she felt kind of bullied into confessing to being behind one of the accounts.

“I personally think the Texas Rangers have bigger and better crimes to fight,” she said.