More than half of workers in the state’s Department of Correction— about 3,000 — have refused a coronavirus vaccine, according to state data.

The workers are part of the more than 5,400 correctional personnel and contracted healthcare staff employed across the state prison system.

Corrections officials say some of the employees may have been vaccinated elsewhere and that the department is working to educate employees about the benefits of the vaccine.

But prisoners advocates say the significant number of refusals reflect a weaknesses in a system that has contributed to the deaths of at least 19 people in the state’s prisons, with a population of about 6,500.

Another two people have died in the county jails, which house another 6,000 people waiting for trial or sentenced to shorter amounts of time.

“The way that the virus has gotten in to prisons and jails is through staff,” said Elizabeth Matos, executive director of the Boston-based nonprofit Prisoners' Legal Services, which works with people behind bars. “If staff are not getting vaccinated in large numbers, then the virus will keep coming in.”

The DOC data was released as part of an order by the state Supreme Judicial Court in an ongoing case filed by prisoner advocates concerned about the spread of COVID-19.

Most county jails have yet to file reports on staff who have refused a vaccine. On Monday, a spokesperson for the Massachusetts Sheriffs’ Association said that sheriffs offices, which run the county jails, are still collecting data.

Matos said she was not surprised that DOC data showed a significant number of employees refusing vaccinations. Prisoners tell her about staff who refuse to wear masks and others who advise them to refuse the vaccine, she said.

Nearly 2,000 prisoners, or about a third of the DOC prison population, also has declined the vaccine, according to state data.

“This has been a problem for a number of our clients who feel like they have legitimate trust issues or they have medical concerns around allergic reactions,’’ she said. “A lot of those questions have not been addressed adequately yet.”

Katy Naples-Mitchell, a staff attorney with the Charles Hamilton Houston Institute for Race & Justice at Harvard Law School, says correctional staff should be required to be vaccinated as part of their employment.

At the same time, she says because of the lackluster number of vaccinations and an increase in COVID-19 variants, government officials should focus on reducing prison populations to stop the spread. Currently, there are more than 350 active cases of COVID-19 among prisoners statewide.

“The state has a responsibility to make sure that people in its custody are safe,’’ she said.