Members of the Boston Fire and Police departments work in deteriorating facilities beset by mold, cracks, and failing infrastructure, according to a pair of audits commissioned by the city and released this week.

“Many facilities are in dire need of replacement or upgrades,’’ the audit of the Boston Police Department said.

The long-awaited audits urged broad organizational improvements at the city’s two largest public safety agencies, enhanced efficiency in managing off-duty shifts, and upgraded training for uniformed personnel.

Samuel R. Tyler, president of the Boston Municipal Research Bureau, said the audit failed to take a strong enough position on whether the Fire Department could be fiscally leaner, by, for example, consolidating fire stations that are close to each other.

“I would have liked to see more of an emphasis on how we can make the Boston Fire Department much more efficient,’’ Tyler said. “The Boston Fire Department . . . is one of the most expensive fire departments in the country. How do we control spending? How do we control overtime?’’

Fire Commissioner Joseph Finn, calling the audit a blueprint for the next five years, said it fairly reflects long-term neglect of firehouses. He said he instituted significant overhauls soon after taking office, such as refining work schedules and limiting the practice of firefighters swapping shifts. He said the department has been operating with fewer people than it had 12 years ago, without sacrificing service.

“The proof is in the pudding. We have the lowest fire death rates in the country . . . and that’s not a mistake,’’ Finn said.

The audits were initiated by Mayor Martin J. Walsh after he took office in 2014, in an effort to assess the effectiveness of major city departments. The mayor ordered nine audits, including two for the Boston Redevelopment Authority, at a total cost of $2.2 million.

The city paid $84,200 to Public Safety Strategies Group of West Townsend to review the Police Department, which employs 2,200 uniformed members and 750 civilians. The company submitted a 63-page report, dated Dec. 1, 2015, to the mayor’s office. The Globe received the report Tuesday.

The report lauded the agency for being proficient in managing large-scale events and for its engagement with the community.

But it criticized the department for exercising little control over assigning overtime and having an ineffective process for scheduling off-duty details for officers hired to stand watch, for example, at construction sites.

The report said diversity levels have not changed significantly despite efforts to make the department more closely reflect an increasingly diverse community. The audit urged a recruiting plan with messages targeting certain neighborhoods.

The report also took aim at the department’s Community Ombudsman Oversight Panel, whose three volunteers are appointed by the mayor and can review cases appealed by people who filed complaints against the police. Many of the panel’s policies and procedures for internal investigations are out of date, the cases and scope of the their reviews are limited, and panel members say they have little authority, the audit said.

The audit painted a grim picture of the Police Department’s 23 facilities, including 11 police stations. Some stations lack secure interview rooms, areas specifically designated for prisoners, and spots for officers to write their reports.

Police spokesman Lieutenant Michael McCarthy said the department is already taking steps to address many of the audit’s findings, including proposing long-term facility improvements in the next budget.

New volunteers for the Community Ombudsman Oversight Panel have been appointed, and Commissioner William B. Evans is working with the Internal Affairs Division to increase the panel’s caseload without overburdening its members, McCarthy said.

McCarthy highlighted the department’s new cadet program, which now has more than 351 applicants, as one prominent effort to increase diversity. More than half of the applicants are people of color.

The audit of the Fire Department, conducted by Matrix Consulting Group, of Mountain View, Calif., cost $90,000.

The company’s report, dated July 7, 2015, has been submitted to the mayor. The Globe received the audit Monday after requesting it for months.

The report addressed the administrative side of running the Fire Department — such as boosting staff, business practices, and technology. Outdated information systems impede the department’s ability to track and control personnel and costs, the audit found.

Meghan E. Irons can be reached at meghan.irons@globe.com.