"One's racial identity is not a qualifying criteria or disqualifying standard for NAACP leadership," the NAACP said in a statement today.
On the city application form, Dolezal identified herself as white, black and American Indian, ABC affiliate KXLY in Spokane reported. The city has said it is investigating whether her claims violated any city policies.
But Ruthanne and Lawrence Dolezal told KXLY that Dolezal is their biological daughter and they are both white.
When a KXLY reporter asked Rachel Dolezal Wednesday, "Are your parents white?" Dolezal removed her microphone and walked away, KXLY said.
ABC News' attempts to reach Rachel, Ruthanne and Lawrence Dolezal today were unsuccessful.
Amid it all, Dolezal became the center of a social media frenzy, and #RachelDolezal was the No. 1 trending topic on Twitter.
Reactions included anger over her possible misrepresentations -- but also apparent sympathy.
Some commenters even brought up the recent gender transformation of ex-Olympian Caitlyn Jenner, formerly Bruce Jenner.
Even a celebrity weighed in.
Though Dolezal's application for the city position is being examined, her racial claims may not be an issue for the NAACP.
"For 106 years, the National Association for the Advancement of Colored People has held a long and proud tradition of receiving support from people of all faiths, races, colors and creeds," the group's statement said. "NAACP Spokane Washington Branch President Rachel Dolezal is enduring a legal issue with her family, and we respect her privacy in this matter.
"The NAACP Alaska-Oregon-Washington State Conference stands behind Ms. Dolezal's advocacy record," the group added. "In every corner of this country, the NAACP remains committed to securing political, educational and economic justice for all people, and we encourage Americans of all stripes to become members and serve as leaders in our organization."
The NAACP Spokane chapter led by Dolezal did not immediately respond to ABC News' request for comment.
Spokane Mayor David Condon and City Council President Ben Stuckart said in a statement: "We are committed to independent citizen oversight and take very seriously the concerns raised regarding the chair of the independent citizen police ombudsman commission. We are gathering facts to determine if any city policies related to volunteer boards and commissions have been violated. That information will be reviewed by the City Council, which has oversight of city boards and commissions."