PROVIDENCE, R.I. (AP) — Rhode Island hasn’t shared any mental health records with the federal background check system used to screen prospective gun buyers, contributing to what gun control advocates call major gaps in the database.

State police Chief Col. Steven O'Donnell said his agency and other state leaders have been ‘‘brainstorming’’ the best way to share such records with the FBI’s background check system but that the process is ongoing.

‘‘We are working with all the stakeholders, trying to figure out what the best policy is to move forward,’’ he said recently. ‘‘Obviously it’s a concern of ours, but obviously you want to get it right.’’

States voluntarily submit information to the background check system, which screens available records to see if a person is prohibited under federal law from having a gun. People who have been convicted of felonies or domestic violence or are the subjects of restraining orders may not purchase guns, for instance; those who have been committed to mental institutions or have certain drug convictions also are prohibited.

Christine Hunsinger, a spokeswoman for Gov. Lincoln Chafee, said Monday that a working group including law enforcement, public safety and health officials and General Assembly staff is looking at potential ‘‘gaps’’ in Rhode Island law on the issue of gun safety and whether new legislation is needed.

‘‘This is one of those areas that is under review to fully understand where Rhode Island is now, what the law requires and what the necessary steps are to get Rhode Island to where it needs to be,’’ she said of the submission of mental health records to the FBI database.

Amy Kempe, a spokeswoman for Attorney General Peter Kilmartin, said the group is trying to address questions about which mental health records should be shared and how to comply with state and federal privacy laws.

‘‘These are the policy and legislative decisions that need to be discussed,’’ she said.

Last month, President Barack Obama proposed sweeping gun control measures that include incentives for states to share information with the background check system.

The coalition Mayors Against Illegal Guns says the FBI background check system has blocked more than 1.9 million sales and permit applications since 1999, when it was created. But the group, co-chaired by New York’s Michael Bloomberg and Boston’s Tom Menino, says there are still ‘‘serious gaps and limitations’’ in the data because not all states are sharing comprehensive information.

A November 2011 report by Mayors Against Illegal Guns found that 23 states and the District of Columbia had submitted fewer than 100 mental health records to the database and that 17 states had submitted fewer than 10. Four states, including Rhode Island, had submitted none.

Nine of the 10 states that had submitted the most records per capita had adopted laws or policies that allowed or mandated the sharing of the records with the FBI system, the report said.

The report cited ‘‘lack of funding’’ to update software or implement record-sharing as a major obstacle in Rhode Island.

O'Donnell, the police chief, declined to address specific barriers, saying only the working group is trying to come up with the ‘‘proper rules.’’

Providence Mayor Angel Taveras, a member of Mayors Against Illegal Guns, said through a spokesman Monday he supports record-sharing and believes the state should ‘‘make it happen.’’

State Rep. Patricia Morgan, from West Warwick, called the state’s inaction to date on the submission of mental health records ‘‘inexcusable.’’