The city’s biggest labor union is crying foul over City Hall’s demand that bilingual workers take a test in the language that they are being paid extra to speak.

It’s no small matter.

According to the city controller, San Francisco paid out about $2.7 million in incentive pay last year to police, firefighters, social workers, clerks and staffers who are fluent in Chinese, Spanish, Russian, Arabic, Vietnamese and other languages needed to better communicate with the city’s various immigrant populations.

It’s one of a number of “extra pay” benefits built into city contracts — they also come into play for working at night, performing as a supervisor or even being assigned to a city sewage plant.

But now the Service Employees International Union Local 1021, which represents a majority of the 2,400 workers earning the bilingual pay, claims the city is going too far in its effort to tighten up on who gets the extra money and who doesn’t.

“The city has never required that employees who already receive a bilingual pay differential take an examination” to keep their pay, SEIU field supervisor Xiu Min Li wrote in a complaint filed late last month with the state Public Employment Relations Board, which polices the contracts of government union workers.

The bilingual boost can mean an extra $80 or $120 a month for about 1,700 SEIU members, depending on how many hours they use their second language on the job.

The dispute began months ago when the city’s Human Resources Department discovered that, because of record-keeping errors, it didn’t have language certification records for 55 of the workers being paid. All of the workers belong to SEIU.

In June, the city began calling in the workers for testing. Depending on their job requirements, the tests varied from demonstrating simple speaking skills to detailed, written proficiency.

“We are checking to make sure everyone has the skills they are being paid for,” said Susan Gard, policy chief for the Human Resources Department.

According to Gard, 39 workers passed, six failed and seven refused to take their tests. Three others are waiting for new tests to be designed.

On Aug. 23, the SEIU filed an unfair labor practice complaint with the Public Employment Relations Board, demanding that the city “cease and desist” from carrying out the new testing requirement.

The union noted, among other things, that the city lacks a uniform test for all languages.

“We don’t have an issue with people being certified to get paid for bilingual work,” said SEIU’s Li. “The problem is the city haphazardly administered the program ... and suddenly they’re issuing a letter saying you have to be tested again if want to get paid.”

Gard countered that no one’s pay has been cut while the negotiations are continuing with the union and that the SEIU acted prematurely in filing the unfair labor practice charge.

Other unions, such as the Police Officers Association, have no problem with the tests. In fact, the POA’s new contract calls for bilingual officers to be tested every three years.

“We are completely fine with that to receive the proper compensation,” said Martin Halloran, the POA’s past president who still works for the union.

As usual, there appears to be plenty more at play between the SEIU and the city than just testing for bilingual pay.

According to Li, City Hall has repeatedly acted “unilaterally” — whether creating a Department of Homeless and Supportive Services without consulting the union or sending out a notice to city workers requiring them to resubmit documents to keep collecting dependent benefits.

“We feel we need to take a stand,” Li said.

And apparently, the union got the city’s attention. Late Tuesday, the two sides reached a deal to allow workers who failed their test to retake them, in exchange for the union dropping the state complaint.

Tuff sell: Oakland Mayor Libby Schaaf just barely won approval Monday night for her Tuff Shed village near Lake Merritt.

Five Oakland City Council members — Noel Gallo, Dan Kalb, Larry Reid, Annie Campbell Washington and Abel Guillen — voted yes, while Desley Brooks and Lynette Gibson McElhaney were absent, and Rebecca Kaplan abstained.

Kaplan said the mayor’s strategy to set up 20 of the prefab sheds in the parking lot of the boarded-up Kaiser Convention Center failed to include plans for sanctioned homeless RV parking and the use of church parking lots for temporary housing.

“Instead, they brought up a proposal to help a tiny fraction of the people” at a higher cost, she said.

The Lake Merritt sheds are being installed with mostly private funds at a cost of about $200,000, but will require as much as $750,000 a year in city and other money to operate, according to Joe DeVries, an assistant to the city administrator who works on homeless issues.

Schaaf said that while the sheds may not be perfect, “we can’t afford to sit around and do nothing. The inhumane response is inaction.”

Oakland’s growing homeless problem has become one of the key issues in the November city elections — including Schaaf’s own re-election bid.

Kaplan has endorsed Schaaf rival Cat Brooks in the Oakland mayor’s race.

San Francisco Chronicle columnists Phillip Matier and Andrew Ross appear Sundays, Mondays and Wednesdays. Matier can be seen on the KPIX TV morning and evening news. He can also be heard on KCBS radio Monday through Friday at 7:50 a.m. and 5:50 p.m. Got a tip? Call 415-777-8815, or email matierandross@sfchronicle.com. Twitter: @matierandross