Mayor Bill de Blasio’s wife is claiming credit for a scoring permanent city funding for a cash-strapped, black cultural institution — saving it from closure — all in the name of trying to become Brooklyn’s next borough president, critics charge.

City Hall sources told The Post that first lady Chirlane McCray had nothing to do with the Weeksville Heritage Center in Crown Heights — which pays homage to the historic site of one of the nation’s first communities of free black people — securing a key city designation last year to receive permanent government funding.

However, they said that hasn’t stopped the mayor’s office from trying to use its political muscle to position McCray — a 2021 borough president hopeful — front and center during a ceremony next week celebrating the museum’s new designation.

“I think without question the way the administration is handling this event is to promote the first lady and her interest in becoming Brooklyn borough president,” said one insider.

“As someone who’s aware of the intense negotiations that went on with Weeksville, the first lady wasn’t involved, so it really takes away from the real work and effort done by the council members and others who devoted a lot of time and energy.”

The de Blasio administration initially planned to honor Weeksville Heritage Center with the designation during a gala ceremony in February, which is Black History Month. But a source said City Hall postponed the event following complaints that the date was selected to accommodate McCray’s schedule —  without accounting for work schedules of local lawmakers and community leaders “who truly led the fight.”

The ceremony has been rescheduled for March 13 at the center on Buffalo Avenue.

McCray still appears to be getting top billing based on emails sent out by the mayor’s office this week to lawmakers and other dignitaries.

“Please join NYC First Lady Chirlane McCray, [Weeksville] Executive Director Rob Fields, and supporters … at Weeksville Heritage Center … to celebrate the addition of this remarkable organization to the New York City Cultural Institutions Group,” said one email obtained by The Post.

City Hall spokeswoman Jaclyn Rothenberg adamantly denied that McCray is trying to steal the limelight or use the ceremony to boost her political career. She said the administration initially wanted to hold the ceremony in February “because it’s Black History Month,” but “we were happy to change the date” to accommodate lawmakers’ schedules.

The heritage center celebrates the pre-Civil War, African-American community of Weeksville, Brooklyn — between Crown Heights and Brownsville — which had more than 500 residents in the 1850s.

Following a budget shortfall, the center was nearly forced to close last year, and only managed to stay afloat after raising more than $271,000 through an online campaign.

The Weeksville center has historically received various pots of government funding piecemeal, including $456,000 from the city last year.

City Council Speaker Corey Johnson and Brooklyn council members Robert Cornegy and Laurie Cumbo helped lead the charge to convince the Department of Cultural Affairs to include Weeksville with 33 other museums, theaters, concert halls, botanical gardens and zoos that comprise the city’s “Cultural Institutions Group.”

These institutions — which include Manhattan’s Metropolitan Museum of Art and Carnegie Hall — operate on city-owned land and receive taxpayer money to fund its operations and subsidize energy costs. Most have a long history of lacking workplace diversity and are saturated with mostly white workers.

“We’re thrilled that First Lady McCray, who’s visited Weeksville in the past, accepted my invitation, and will be here … to represent the administration, and mark this special occasion with us, along with members of the City Council and other elected officials,” Fields said.

Johnson said the “City Council was proud to push the administration to make the Weeksville Heritage Center a member of the Cultural Institutions Group.”

“Weeksville is a crucial part of Brooklyn’s cultural scene that celebrates New York City’s rich African American legacy,” he added.

Cornegy, who is running for borough president, declined comment.

Cumbo did not return messages.