An 81-year-old resident of a ­Salem nursing home shot and killed himself with his own legally registered handgun — a death that state and local law enforcement officials said Tuesday is as troubling as it is mystifying.

The man, whom officials declined to identify, shot himself shortly after 10 p.m. Friday at the Grosvenor Park Health Center, ­Salem police said.

Suicides in nursing homes are unusual, and those involving guns are rarer still, according to the few studies delving into the matter.

Law enforcement and health authorities are investigating the shooting at the nursing home, which is owned by Synergy Health Centers. That New Jersey company has been the subject of a series of actions by regulators, who have imposed fines totaling hundreds of thousands of dollars following deaths and substandard care at other facilities.

At Grosvenor Park, a nursing supervisor Friday night heard what sounded like a gunshot, ran to a room, and found the man sitting in a chair with a gun in his hand, Salem Police Captain Conrad Prosniewski said.

“One of the big questions is,’’ Prosniewski said, “what’s a gun doing in a nursing home?’’

Officials declined to release many details about the death, citing their ongoing investigation. So it is not clear whether the man left a suicide note.

“It is still under investigation, but right now it appears it was a suicide,’’ Prosniewski said.

Synergy, which owns 11 Massachusetts nursing homes including the 123-bed Grosvenor Park, said in a statement guns are prohibited on its properties.

“Concurrently, we are conducting our own internal investigation to fully understand the facts and determine if there are any steps we should take to prevent a similar incident from occurring in the future,’’ the statement said.

The company said a member of Grosvenor Park’s clinical team had conducted a routine medical check on the man an hour before the incident happened. The statement said nursing home staff immediately contacted emergency medical professionals and the police after the shooting, and reported the death to the state Department of Public Health, which regulates nursing homes.

“We can say with confidence that there is no threat to the safety of our residents or our employees,’’ the statement said.

Grosvenor is offering grief counseling to residents and workers, a spokesman said.

State health department spokesman Tom Lyons said in a statement the goal of his agency’s review “will be to ensure the facility has taken appropriate action to meet the needs of its residents and ensure their safety going forward.’’

Grosvenor Park has historically received high marks from state inspectors, and still ranks among the top 4 percent of Massachusetts nursing homes one year after Synergy purchased the longtime family owned facility, according to state records.

Nursing homes are required to report suicides to the health department. That agency was unable to say how many nursing home suicides have been reported in recent years but could find none since 2010 that might have involved a firearm.

Research involving nursing homes suicides is scarce.

A study published last year in the International Journal of Geriatric Psychiatry found 113 nursing home suicides between 1949 and 2013 detailed in medical literature, mostly in the United States.

The researchers found most of those committing suicide were men 61 to 93 years old, and the vast majority hung themselves or jumped. Just one review mentioned a nursing home suicide involving a firearm — in a nursing home in Finland, by an 81-year-old man.

Similarly, a study of New York nursing home deaths between 1990 and 2005 found 47 suicides, mostly due to “long falls,’’ and few by firearms.

Dr. Rob Schreiber, medical director of evidence-based programs at Hebrew SeniorLife, said he routinely asks about access to guns when he visits patients at their homes. But he said it never occurred to him to ask the same question at the company’s three nursing homes in Greater Boston.

After hearing about the suicide at Grosvenor, Schreiber said he is rethinking that approach.

“It’s a different world, and we have to start thinking differently,’’ Schreiber said. “I am definitely going to do it now.’’

Kay Lazar can be reached at kay.lazar@globe.com.