A cost-saving initiative that brought private organizations into four Boston community centers lacks valid contracts, financial audits, and safeguards to confirm that outside groups perform background checks on their employees, according to a report issued Monday by a city watchdog.

The report by the Boston Finance Commission also raised questions about liability insurance and whether arrangements with private groups actually saved taxpayer money because the city continued to pay for utilities, maintenance, and repairs.

“We’re not against them leasing out the community centers so long as binding contracts are in place,’’ said the finance commission’s executive director, Matthew Cahill. “Costs to the taxpayers need to be offset, and the city must verify that people are living up to their obligations.’’

Investigators did not find employees at the community centers who failed criminal background checks, but the city has not verified that workers have been screened, Cahill said. Organizations contacted by the Globe said all employees and volunteers pass rigorous scrutiny, including a check of criminal records.

Mayor Martin J. Walsh’s administration declined Monday to respond to the report or say what steps it would take to verify that employees working in the centers had undergone proper background checks.

“The city is reviewing the report and will be working with [Boston Centers for Youth and Families] to determine next steps,’’ Walsh’s spokeswoman, Laura Oggeri, said in an e-mail.

In 2010, the city faced layoffs in the depths of a recession. The Globe reported at the time that then Mayor Thomas M. Menino cut staff at several community centers but tried to preserve activities by partnering with private organizations.

The commission’s report mentioned the Orchard Gardens Community Center in Roxbury, run by the Boys & Girls Club of Boston; Thomas Johnson Community Center on Annunciation Road, operated by Smart from the Start; the Walsh Community Center in South Boston, overseen by the Gavin Foundation; and the Stillman Tennis Center, which is administered by Charlestown Against Drugs.

Investigators from the Boston Finance Committee, an independent body created more than a century ago by the state Legislature, began an inquiry when repairs to the tennis center’s heating system raised questions, Cahill said. Records showed the city had been paying roughly $20,000 to erect an inflatable bubble over three courts that allowed tennis to continue through the winter. The city also paid for repairs, electricity, and utilities to heat the bubble.

The report said investigators determined there was no formal contract between the city and Charlestown Against Drugs to operate the tennis bubble.

The organization’s treasurer, Thomas Desmond, said that under Menino, the city agreed to pay for utilities and put up the bubble. Charlestown Against Drugs is a volunteer organization, Desmond said.

“The only people that are paid are the tennis professionals we hire to provide affordable lessons,’’ Desmond said. “The key was to keep the price low so people can take advantage of it.’’

The group has liability insurance, Desmond said. While part of the mission is to help people get back on their feet, all employees are thoroughly screened, Desmond said.

“I’m very proud of the way we run it,’’ Desmond said. “That tennis bubble has saved a lot of kids’ lives.’’

Andrew Ryan can be reached at acryan@globe.com.