“Local law enforcement is just chasing Latinos all over the place for tiny traffic infractions,” said Adelina Nicholls, the executive director of the Georgia Latino Alliance for Human Rights.

But to Butch Conway, the longtime sheriff of Gwinnett County, there is no reason his deputies should not turn in immigrants caught driving without a license. They are, after all, doubly breaking the law.

“I find it offensive that they just thumb their nose at our laws and operate vehicles they are not licensed to operate,” Mr. Conway said in a 2010 interview, “on top of the fact that they are here illegally.” (Through a spokeswoman, he declined to comment for this article.)

In nearby Cobb County, Maria Hernandez, a school janitor from Mexico, was arrested while driving home from work one night in May. An officer conducting a random license tag check, a common practice in some police departments, had determined through a state database that the tag had been suspended because the car lacked insurance. After pulling over Ms. Hernandez, the officer then discovered she had no driver’s license.

Her boss tried to bail her out of the Cobb County jail, but was told that the money would go to waste: She was headed to immigration detention, where she would spend three days trying to explain that she was a single mother with a sick child. Estefania, her 13-year-old daughter, was being treated for depression after a suicide attempt.

Ms. Hernandez was released, given an ankle monitor and told to report back with a plane ticket. (A lawyer has helped delay the deportation.)

Her car, in fact, was insured; the officer had called in the wrong license tag, according to a Cobb County Police Department spokesman, Sgt. Dana Pierce.