The internal investigators found no evidence that the female officer "granted or would have granted permission" to share the image.
In a second incident, Findlay received an image of two female subordinates in bikinis, according to the letter. He showed the image to at least one other male officer, and later to another male who was professionally acquainted with one of the subordinates during an out-of-state business trip, the letter adds.
This came to the same subordinate's attention after an officer from another jurisdiction told her.
Internal affairs investigated the incidents, and Burbank concluded that the allegations had been sustained.
"Your behavior calls into question not only your personal professionalism but that of the entire police department," Burbank wrote in his letter.
The chief noted that Findlay's contributions to the force during his career have been "significant," and that "it is unfortunate that your lack of judgment in this instance has such adverse effects."
The chief wrote that Findlay's conduct called into question his ability to remain a leader in the department, but that "your conduct did not rise to the level of termination."
Burbank noted that Findlay had decided to resign from the department.
"By accepting your resignation, I deem this matter concluded," Burbank wrote in the letter, which was obtained Friday by The Tribune through a records request.
The police department in February had denied a Tribune records request for police department internal affairs reports discussing Findlay's case, saying it could hamper a pending investigation. The newspaper renewed its request on Friday and was told that document was still being processed and would be provided when complete.
City records show Findlay started at the police department June 1, 1994.
Utah police officers who started during that era become eligible for a number of retirement benefits after 20 years of employment.
Had Findlay been terminated or left Salt Lake City police prior to this month, he would have had to find a job with another police force to gain those retirement benefits.