A 39-year-old public assistance caseworker for Montgomery County was shot four times yesterday morning during an argument with her estranged husband in the parking lot of the Rockville building where she is employed, county police reported.

Ernest W. Carter, 54, the estranged husband of the victim, Jean Ann Carter, of Rockville, was arrested shortly afterward and charged with assault with intent to murder and use of a handgun in the commission of a crime, police said.

Mrs. Carter was in critical condition at Suburban Hospital.

Carter, of 15811 Good Hope Dr., Colesville, was being held at the County Detention Center last night on $25,000 bond.

Officers quoted witnesses as saying that the Carters were arguing loudly as they got out of a car in the parking lot of the building at 5630 Fishers La. around 8:15 a.m. Ernest Carter allegedly returned to his car, got a revolver and fired about three shots from a distance of eight feet, according to police.

Jean Carter, struck by at least one of the first shots, fell against the car and her husband fired again, police said. When she fell, Ernest Carter fired once more, police reported.

Carter was arrested at 9:10 a.m. at the Columbia Country Club in Chevy Chase, where he is chief maintenance engineer and manager of the bowling alley.

Timothy Clemons, 16, who said the court appointed Ernest Carter as his guardian three months ago, said the Carters separated on Dec. 1, but remained "on friendly terms."

"I'd thought there was a good chance they would get back together," he said.