ARIVACA, Ariz. — Every time Jack Driscoll drives the 32 miles from this remote outpost in southeastern Arizona to the closest supermarket, or to doctor’s appointments, or to a pharmacy to fill his prescriptions, he must stop at a Border Patrol checkpoint and answer the same question: “Are you a U.S. citizen?”

Sometimes, Border Patrol agents ask where he is going or coming from, the type of car he is driving, what is in that bag on the back seat or what brings him to these parts, even though he has lived here for more than a year. Lately Mr. Driscoll, a 75-year-old retired highway construction engineer, has taken to opening his window just a crack and yelling, “I’m American,” as he stops at the checkpoint, one of the ways he has found to protest.

He is not the only one in this community of 800 whose anger is boiling over. Although checkpoints are a fact of life here — the tollbooth-like way stations are part of the routine for anyone driving the highways near the border — citizens like Mr. Driscoll are now starting to raise questions about whether the familiar but irritating routine violates their constitutional rights, which include protections against arbitrary stops and searches.

“I’m a mostly honest person,” Mr. Driscoll said in an interview at the library here, his arms crossed over his chest. “I worked hard all my life. I paid my taxes. I even stop at stop signs, and I feel like they treat me like a criminal.”