BOSTON — The city is scrutinizing a longstanding agreement that allows the Red Sox to use a public street abutting Fenway Park for free game-day parking for players, their families and staff.

New Mayor Martin Walsh’s administration may ask the team to pay for use of Van Ness Street on game days.

“We are currently reviewing the agreement, and compensation is one of the issues that we will consider during this review,” Walsh spokeswoman Kate Norton said of the “public safety order” city officials signed in October giving the Red Sox permission to seal off Van Ness Street on game days. The deal was signed under the administration of Walsh’s predecessor, Thomas Menino.

In 1945, then-team owner Tow Yawkey signed a deal with the city allowing for the game-day closure of Van Ness Street, according to a statement from the World Series champions, although there appears to be no paper records of the pact.

The team says it’s a public safety issue, allowing ambulances easy access to Fenway along Van Ness and giving players safe access to the park.

“City public safety agencies have determined that for public safety purposes, it is advantageous and appropriate to have Van Ness Street closed to vehicular traffic during Fenway Park events,” the team statement said.

A public watchdog criticized the contract.

“This is another precious gem dropped into the Red Sox basket at the expense of the taxpayers,” said Gregory Sullivan, the state’s former inspector general who’s now research director of the Pioneer Institute.

The Walsh administration is also reviewing a separate deal that allows the team to close Yawkey Way on game days to sell beer, food and other concessions. The city gets $7.3 million over 10 years under that deal.