BELFAST  — A former tax examiner has been formally charged with murder after he fatally shot a woman and injured her son Wednesday night, according to police.

Police identified the woman killed at a Waldo Avenue home in Belfast as 55-year-old Lynn Arsenault of Belfast and Garland.

Her son, Mathew Day, 22, also was found shot in the home. He initially was listed in critical condition, but a Maine State Police commander said Thursday morning at a news conference that Day’s condition had been upgraded to stable. He is being treated at Eastern Maine Medical Center in Bangor, where he had been taken by LifeFlight helicopter.

Todd Gilday, 44, of Belfast is accused of fatally shooting Arsenault, also known as Lynn Day. Gilday additionally is charged with elevated aggravated assault for causing serious injury to Mathew Day. He made his initial appearance Thursday afternoon in Waldo County Superior Court, during which Justice Robert Murray ordered that Gilday be held without bail pending a hearing.

During Thursday’s court appearance, Gilday was represented by Chris MacLean, who was serving as attorney of the day. MacLean told the justice that Gilday’s family intends to hire a defense attorney.

Gilday, a heavyset man who was shackled by the hands and feet, answered Murray’s few questions in a loud, clear voice. He told the justice he understood that if he is convicted of murder, he will serve a prison sentence of 25 years to life.

Murray said that a hearing to determine whether the state will allow bail will be held sometime in the next five days.

Earlier Thursday, a state police commander said at a press conference that investigators believe Gilday knew at least one of the people in the home.

“It’s very important to us to find out how he knew the people,” said Christopher Coleman, commander of the Maine State Police Major Crimes Unit.

Coleman said it was too early to release information about a possible motive for the shootings and that police investigators want to speak to anyone who might have information.

A friend of Day, a man named John Riley, was also in the home at the time of the shootings and was not injured.

In an affidavit in support of arresting and holding Gilday, Detective Ryan Brockway of the Maine State Police Major Crimes Unit wrote that Riley told police that a man had come to the door and opened it partially before Mathew Day tried to close it. Brockway wrote that the “glass was blown out of the door and the door was kicked open.”

The man then shot Arsenault and said he would “kill everyone in the [expletive] house,” the affidavit says.

When police arrived, Day was lying across Arsenault, who died of a gunshot wound to the chest that punctured her lung, according to autopsy results cited in the affidavit filed Thursday.

Day was shot in the arm and stomach with birdshot, the document said.

When asked by Belfast police Sgt. Brian Lunt if he knew who shot him, Day replied, “Todd Gilday,” according to the affidavit. He told Lunt that he did not know why Gilday had shot them.

Police focused on Gilday after receiving two 911 calls reporting the shootings, one from neighbors and the other from Riley. Police notified officials in three other states where Gilday has ties while they searched for him Wednesday night.

Gilday went to Pen Bay Medical Center in Rockport sometime overnight to check himself in, Maine Department of Public Safety spokesman Stephen McCausland said.

Gilday was arrested without incident about 8 a.m. Thursday at the hospital and charged with murder.

The car police said Gilday was driving — a gray 2007 Nissan Altima with a Maine lobster plate reading “FOREX” — was found parked in the parking space nearest to the entrance of the Pen Bay emergency room.

His car was seized and taken to the state police crime lab in Augusta for examination, McCausland said.

Belfast police and the Waldo County Sheriff’s Office went to the scene of the shooting at 11 p.m. Wednesday. A neighbor of the victims said he first heard arguing late Wednesday night in the run-down yellow house on Waldo Avenue, then a gunshot, then a woman screaming.

Although he and his family were accustomed to hearing arguments and fighting in the house next door, Wednesday night was “pretty intense” and much worse than usual, the neighbor said, adding that he did not feel comfortable sharing his name.

In the affidavit, Brockway wrote that Arsenault stayed with her son on the days she worked at Bank of America in Belfast.

A Bank of America spokesman said that Arsenault had worked at the Belfast call center for 10 years and most recently led a team that processes credit card applications.

“We’re shocked by this tragic news. Our thoughts are with Lynn’s family,” T.J. Crawford said. “We have grief counselors available at our call center throughout the day. She was close with many of her co-workers.”

Eric Sanders of Belfast, who used to work with Arsenault at Bank of America, said Thursday that her murder is a shocking tragedy. The Belfast city councilor described Arsenault as a hardworking woman who cared a lot about her co-workers.

“She was a wonderful lady,” he said. “Her team was like family to her. She cared very much about the people she worked with. … It’s got to be heartbreaking for anyone who worked with her.”

Sanders said the many questions surrounding Arsenault’s death are disconcerting.

“In sleepy little Belfast … it just makes you wonder why,” he said.

Arsenault’s daughter-in-law said Thursday that family members were still being interviewed by police and weren’t able to speak with the media.

The neighbors said they were used to calling police to report fighting and noise from the house.

“Lynn was a nice lady,” one neighbor said, adding that the woman was concerned about her son.

Mathew Day had been arrested in late May in Belfast and charged with aggravated assault and domestic violence criminal threatening.

According to a report from the Belfast Police Department, his alleged victim, with whom he was romantically involved, had gone to his home, where the couple got into an argument. She told police later that Day had grabbed her by the neck while she was leaving, which caused her to nearly lose consciousness.

Day was scheduled to appear Thursday morning at Waldo County Superior Court after being indicted earlier this month by a grand jury on the aggravated assault and domestic violence assault charges.

Beginning late Wednesday, Maine State Police troopers kept an eye on the neighborhood overnight, according to the woman who lived next door to the yellow house.

According to a LinkedIn profile associated with Gilday, he worked as a tax examiner for Maine Revenue Services. The profile also says he is the owner of Spinnaker Financial LLC and that he has worked in sales for health insurance companies with a specialty in Medicare. He said he was educated at Sotheby’s Institute of Art, the University of Phoenix and Rutgers University.

Gilday’s employment with Maine Revenue Services ended last month, according to David Heidrich, assistant director of communications with the Department of Administrative and Financial Services.

A criminal background check showed that Gilday had no criminal history in Maine.