Homeowners who live in San Francisco’s gated Presidio Terrace have been using up to 1 million gallons of city water a year to maintain the picture-perfect trees, walkways and flower beds along their private street — and the city has been paying the bill.

In fact, San Francisco water officials said they have no record of ever having sent a bill to the Presidio Terrace Homeowners Association for water service to the private compound’s common areas for the entire 113 years of its existence.

“It looks like that one just fell through the cracks,” said Public Works General Manager Mohammed Nuru, whose department has been picking up the tab for the Presidio Terrace water bill for the past decade.

According to city Public Utilities Commission records, since 2007 the street has used 12.3 million gallons of water — roughly equal to a dozen football fields 10 feet deep in water.

The annual cost to taxpayers has varied from $2,716 in 2009 to $11,208 in 2017. The 10-year-plus total was $59,548.

The discovery of the water giveaway comes just four months after the San Francisco Board of Supervisors voted 7-4 to overturn the tax auction sale of the tony street — once home to both U.S. Senator Dianne Feinstein and House Minority Leader Nancy Pelosi — after the homeowners association failed to pay $994 in back taxes.

It turned out that the $4.28-a-year tax bill was being mailed to a wrong address and the homeowners’ association never informed the city of the change.

The property was snatched up, at least temporarily, by a couple from the South Bay, Tina Lam and Michael Chang. They paid $90,100, but were forced by the supervisors’ vote to return the street. The couple is now suing to get the street back.

The water flub, however, falls more directly into the city’s lap.

For starters, although Presidio Terrace was built in 1905, there are no water records on the street until 1985, when somebody — PUC officials don’t know who — applied for a water line hook-up.

A water meter was eventually installed in 1999, but the water department has no record of ever having billed anyone for the service. Instead, the bill was designated as belonging to a “non-paying” account, meaning the city PUC simply ate the costs.

In 2007, as part of a change in the city’s accounting procedures, the bill was sent over to the San Francisco Public Works, which handles maintenance of public spaces.

“The city had hundreds of water meters all over the city for places that appeared to be public spaces,” Nuru said.

He said Public Works only recently discovered that the meter was serving Presidio Terrace while doing an inventory of the department’s water use and costs in response to the past drought.

Presidio Terrace is one of a half dozen private property accounts that Public Works is working to transfer to the appropriate owners.

Two weeks ago, we contacted Scott Emblidge, the attorney for the Presidio Terrace Homeowners Association, to ask about the use of city water. Emblidge said he knew nothing about the water bill.

This past weekend, however, a representative of the group called Public Works spokeswoman Rachel Gordon to say they wanted to “get it right with the city.”

And on Monday, the association delivered a $59,548 check to the city.

“They are happy to have worked with the city to have resolved the issue,” said homeowners spokesman Matt Dorsey.

Dorsey said the association had tried to sort out the missing water bills on its own after last year’s tax mess, but that the San Francisco PUC was unable to locate the meter.

Whatever might have happened, said Public Works boss Nuru, “It’s a good story. And we got our money.”

Cops for Alioto: Citing her “common-sense approach,” to city government, the San Francisco Police Officers Association has endorsed Angela Alioto for mayor.

“Her understanding of the city and her commitment for public safety make her the best choice,” said POA President Martin Halloran.

If that’s fact, former Supervisor Alioto was the only choice the union had.

There was no way the POA was going to endorse either Supervisor Jane Kim or former state Sen. Mark Leno , whom they perceive as being anti-police.

The feeling is mutual — neither Kim nor Leno sought the cops’ backing.

And while the union had endorsed Supervisor London Breed in past elections, they pretty much broke ties with her when she joined the call for police reforms after the the police shooting of Mario Woods in the Bayview in 2015.

Alioto, on the other hand, has a long and unbroken record of support for the police union, dating back to her days as a city supervisor in the 1980s and ’90s. She is also supporting the union’s Taser initiative on the June ballot.