CLIFTON, N.J.—A gunman drove across the country to confront his estranged wife, then killed her in a church vestibule as Sunday services let out, authorities said. Two other people were injured in the attack, which sent churchgoers scrambling for safety.

The gunman fled, and authorities were searching for him and warned people that he was believed to be armed. About 200 people were attending services inside St. Thomas Syrian Orthodox Knanaya Church in Clifton when the gunman opened fire before noon. Churchgoers described bedlam after the shots rang out.

“Kids were crying. People were screaming,” Suja Alummoottil told The Record of Bergen County. “It was chaotic.”

Police Detective Capt. Robert Rowan identified the slain woman as 24-year-old Reshma James and the gunman as 27-year-old Joseph M. Pallipurath of Sacramento, Calif.

Police did not identify the other two victims, but Rowan told The Star-Ledger of Newark that all three were shot in the head and that the other two, a 47-year-old woman and 23-year-old man, were in critical condition.

A spokeswoman for St. Joseph’s Regional Medical Center in Paterson, where the victims were being treated, declined to comment on their conditions.

Alummoottil, 40, said Pallipurath appeared angry when he confronted James in the vestibule as the service was concluding. Alummoottil said she went to get help and, a few seconds later, heard three shots. Rowan said James had recently moved from California to New Jersey to escape an abusive marriage and had filed a restraining order against Pallipurath.

Members of the church are mostly first-generation immigrants and their children from the southern Indian state of Kerala, according to the church’s Website.