BOSTON — The Department of Children and Families failed to check whether registered sex offenders were living in or near foster homes and neglected to ensure all children get required medical screenings within seven days of being placed in Massachusetts’ care, according to a state audit released Wednesday.

The agency also could not adequately document that required background checks had been performed on all people living in foster homes, the report from auditor Suzanne Bump found. DCF additionally could not adequately document that the personal information of children in its care was being safeguarded, opening the door to possible identity theft.

Bump said the importance of the audit is not in its tally of how many health checks or background checks are performed, but in DCF’s inability to account for them.

She also pointed to what she called the lack of resources and failure to update computer systems that she said would help managers better supervise staff and ensure that the safety of children is being monitored.

“If it’s not monitored, it’s not detected,” she told reporters.

Bump declined to comment on whether top staff at DCF, including Commissioner Olga Roche, should be removed. She said many of the problems in the report were long-standing and “not of recent vintage.”

The audit covers July 2010 to September 2012, and is not related to the case of Jeremiah Oliver, a 5-year-old Fitchburg boy who is missing and feared dead. The agency has been under intense scrutiny after it was revealed that social workers lost track of the boy, whose family was being monitored by DCF.

The agency released a statement Wednesday saying it was taking steps to make sure that all foster children underwent medical checks and to improve documentation of background checks.

“We are working day in and day out to enhance our ability to protect children and strengthen families,” Roche said in a statement.

Bump noted that some of the recommendations in her report were already being implemented.