Although not formally charged, Campbell posted $2,000 bond in city court in connection with the drunken driving and hit-and-run accusations levied against him.
Phoenix police Sgt. Randy Force said authorities took the 67-year-old into custody on Monday at his home after a two-car collision at a Phoenix intersection.
No one was hurt, but afterward Campbell's BMW continued on.
A witness followed the car, called police on a cell phone and directed them to a home in the Biltmore area, Force said.
"Officers contacted the driver of that BMW who was Glen Campbell," he said. "Based on his appearance and demeanour, they believed he was intoxicated and took him into custody."
In the 1960s, Campbell played guitar with the likes of Dean Martin, the Mamas and the Papas and the Beach Boys. His biggest song was Rhinestone Cowboy.
Although Commissioner Steve Kupiszewski didn't require the singer who has lived in Arizona for 22 years and has no prior convictions to post bond on the assault accusation, Kupiszewski placed Campbell under supervised release.
That could require Campbell to undergo alcohol and drug testing.
Moments before his appearance in front of Kupiszewski, Campbell wearing an Arizona Diamondbacks polo shirt, shorts and tennis shoes seemed relaxed.
"There's a first time for everything," Campbell told his lawyer, Larry Debus.
The other car involved in the collision was driven by Charles Root, 31, a waiter. Root said police took him to a house where he identified a man standing in a yard as the person who hit him. Later, he was told it was the singer.
"It didn't look like him at all. He had on a ball cap and was wearing shorts and a T-shirt," Root told the East Valley Tribune.
Force said that Campbell was also arrested on suspicion of "extreme" drunken driving.
Departmental policy prevents authorities from releasing the results of blood-alcohol tests, Force said, but extreme drunken driving applies when results are above .15. The legal limit for drivers in Arizona is .08.
While being processed at a police precinct on those charges, police said Campbell minutes away from being released to waiting friends and family became angry and kneed Sgt. Bill Niles in the thigh.
Niles was not hurt.
A publicist for Campbell could not be reached for comment.