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A job description for the same position with the Department of Transportation makes clear that program analyst is a nonunion position.

Johnnie Walker, an official with AFGE District 14 and a former president of Local 383, said that Mr. Crawley once was in a certified bargaining unit position but that after a promotion to program analyst his membership should have ended. Instead, officials with the Gray administration concluded they could not force Mr. Crawley out of the union, leaving him free to become an executive board member and attempt to take over the entire bargaining unit.

“This could have been corrected and resolved years ago,” Mr. Walker said.

On Friday, Marcello Muzzatti, president of FOP District of Columbia Lodge No. 1, which includes numerous bargaining units, wrote to Mr. Gray and called Ms. Campbell’s actions “audacious and unlawful.” He asked that Ms. Campbell be recused from the matter, her directives reversed, and that Mr. Crawley be forced to withdraw from the union.

Officials with the Gray administration and Mr. Gray’s office did not respond to written requests for comment.