The suspected gunman was identified as 41-year-old Jiverly Wong of nearby Johnson City, N.Y., a law enforcement official said.
"It obviously was premeditated," said Binghamton Police Chief Joseph Zikuski, noting the gunman blocked the rear exit with his car. "He made sure nobody could escape."
The gunman calmly walked in the front door with two handguns: a 9 millimeter with extended clip and a .45 caliber, CBS News correspondent Bob Orr reports. Sources say he was carrying a satchel with extra ammo, a large knife, a flashlight and what appeared to be survival gear - a sign that he was prepared for a standoff.
Sources told Orr that Wong owned two legally registered guns - but it's not yet known if those were the same weapons used in the spree.
The gunman entered a foyer at the American Civic Association and shot two receptionists, Zikuski said. One receptionist was killed, but another pretended to be dead, then crawled a desk and called 911, he said. Police responded within two minutes.
Zhanar Tokhtabayeva, a 30-year-old from Kazakhstan, said she was in an English class when she heard a shot and her teacher screamed for everyone to go to the storage room.
"I heard the shots, every shot. I heard no screams, just silence, shooting," she said. "I heard shooting, very long time ... and I was thinking, when will this stop? I was thinking that my life was finished."
The gunman entered a room just off the reception area and continued firing, the chief said. He fired on a citizenship class, Rep. Hinchey said.
"People were there in the process of being tested for their citizenship," Hinchey said in a telephone interview. "It was in the middle of a test. He just went in and opened fire."
"We heard four shots when we was in the parking lot -- bam, bam, bam, bam," eyewitness Kenneth Youmans told CBS News correspondent Jeff Glor. "That's when … we see everyone running around and they started getting the dogs, moving us back, telling us we got to get away from the area."
Twenty-six people hid in the boiler room and 37 people were safely removed from the building, Zikuski said. Four people are in critical condition.
Most of the people brought out of the building couldn't speak English, the chief said.
The suspect's body was found with a self-inflicted gunshot wound in an office, according to the law enforcement official who reported the man's identification.
Authorities searched Wont's home friday evening, carrying out three computer hard drives, a brown canvas rifle case, a briefcase, a small suitcase and several paper bags.
Waiting outside a Catholic Charities office where counselors were tending to relatives of victims, Omri Yigal said his wife, Delores, was taking English lessons when the gunman attacked. He had no word on what happened to her.
"At this point, I know the scale of what happened, but I just hope Delores is OK," the Filipino immigrant said. "I haven't got any information. ... The only thing I have right now is hope."
The shooter apparently acted alone although investigators are still questioning a number of people who were inside, reports Orr. The gunman's connection to the center isn't clear, Hinchey said.
"One of the first questions is going to be, what motivated this?" he said. "What caused this to happen? What was the kind of person who did it?"
A woman who answered the phone at a listing for Henry D. Voong said she was Jiverly Voong's sister but would not give her name.
Asked if she was aware that he might have been involved in the shooting, she said: "How? He didn't have a gun. I think somebody involved, not him. I think he got shot by somebody else."
"I think there's a misunderstanding over here because I want to know, too," she said.
The American Civic Association helps immigrants in the Binghamton area with naturalization applications, according to U.S. Citizenship and Immigration Services.
The association describes itself as helping immigrants and refugees with counseling, resettlement, citizenship, family reunification and translators.
Alex Galkin, an immigrant from Uzbekistan, said he was taking English classes this morning when he heard a shot and quickly went to the basement with 20 other people.
"It was just panic," Galkin said.
The association's president, Angela Leach, "is very upset right now," said Mike Chanecka, a friend who answered a call at her home as Leach wept in the background.
"She doesn't know anything; she's as shocked as anyone," Chanecka said. "For some reason, she had the day off today. And she's very worried about her secretary."
At the junction of the Susquehanna and the Chenango rivers, the Binghamton area was the home to Endicott-Johnson shoe company and the birthplace of IBM, which between them employed tens of thousands of workers before the shoe company closed a decade ago and IBM downsized in recent years.