A Boston Police Department tweet honoring Red Auerbach, a white Celtics coach, during Black History Month set off a storm of outrage and criticism that the post was racially insensitive, culturally unaware, and tone deaf.

“Our intention was never to offend,’’ said Lieutenant Detective Michael McCarthy, the department’s spokesman, who also noted its efforts in the past three years to honor black history.

But there are some twists to the Auerbach story.

For one, the Boston Celtics have been showing a video honoring Red Auerbach during Black History Month for the past few years, along with other videos, Celtics officials said.

“The video that discusses Red Auerbach’s legacy is one of a few Black History Month-themed videos we have run during February. Others include one that features Chuck Cooper III, the son of Chuck Cooper who the Celtics selected as the first African-American player to join the NBA,’’ said Christian Megliola, senior vice president of communications for the Celtics, in an e-mail.

The video, shown on rotation during home games at TD Garden, was played again Feb. 4 during the Celtics-Portland Trailblazers matchup — about a week before the Police Department’s tweet.

The Celtics allowed the Globe to view the Red Auerbach video, but Megliola said it could not be posted because it is for use only in the arena.

So far, officials said, there have been no protests of the Auerbach video.

The police tweet did not originate from the video, however. The genesis of that tweet can also be traced to TD Garden — to another tribute to Auerbach and his role in black history.

A Police Department officer had attended an event at the Garden late last month and noticed a bronze plaque on the North Station side of TD Garden, in the Red Auerbach Concourse, said people with first-hand information about the sequence of events. The plaque noted highlights of Auerbach’s career, including the fact he drafted the first African-American player, in 1960, and hired the first African-American coach, Bill Russell, in 1966.

The officer felt inspired to share that information on Twitter, said the people who knew of the incident.

Over the past few years, the department has been commemorating black history. Two years ago, it paid tribute to black officers throughout its history in a photo display at headquarters. Earlier this month, the department tweeted about Russell and Randy Moss, the former New England Patriots receiver who was voted into the NFL Hall of Fame.

But after the Auerbach tweet, the backlash was swift.

The department took it down an hour after it was posted and apologized. A day later, Mayor Martin J. Walsh issued a rebuke, calling it “a gross misrepresentation of how we are honoring Black History Month in Boston.’’

Police Commissioner William B. Evans said the tweet was “insensitive and does not reflect the values of the Boston Police Department.’’

A coalition of civil rights organizations, in a statement, said the tweet “amplifies the need for continued work to deepen our collective understanding of our shared history and the role that Black people have played in it, especially in this city where we consistently stumble on issues of race.’’

After the controversy, Mel King, a political legend and former state representative, said all contributions to black history should be honored.

“I think we need to lift up white people whenever they are doing the right thing,’’ he said.

But King said that he finds it even more important to think about what Russell accomplished: his leadership of the Celtics and his history of dealing with race discrimination in Boston housing and employment.

“How can there be an objection to recognizing someone who brought in a man who accomplished all that?’’ King said.

Darnell Williams, who heads the local Urban League, said he sees nothing wrong with honoring the achievements of white allies of civil rights — but he draws the line at Black History Month.

Williams said “co-mingling’’ histories during such a critical month has drawbacks, especially when blacks have yet to achieve racial parity with whites.

“The reason we went from Black History Week to Black History Month is because black [achievements and contributions] were systematically being excluded and ignored,’’ Williams said. “When we lose sight of the fact that we were excluded from the mainstream, then we will miss the whole point of why Black History Month was created.’’

Meghan E. Irons can be reached at meghan.irons@globe.com. Follow her on Twitter @meghanirons.