Photos posted on social media appeared to show the three officers in front of LAPD headquarters in downtown Los Angeles, purportedly walking to the rally that attracted hundreds of demonstrators on Monday.
Responding to a tweet that included the photos, the inspector general's office tweeted: "Thank you; your tweet has been forwarded to staff in our Complaint Section for processing."
On Tuesday, an LAPD spokesperson told Eyewitness News only that the personnel matter was being investigated and declined to elaborate.
Also on Tuesday, LAPD Chief Michel Moore said that 73% of LAPD employees are fully vaccinated, and another 5% are partially vaccinated.
The city of Los Angeles' deadline is approaching for municipal employees to show proof of full vaccination against COVID-19 or risk termination from their jobs.
Under L.A.'s employee-vaccination mandate, city workers have until Dec. 18 to get vaccinated or apply for a religious or medical exemption.
Monday morning, hundreds gathered in downtown's Grand Park to protest COVID-19 vaccination mandates enacted by the city and other government entities.
The demonstration, dubbed the March for Freedom rally, was held on the same day that the city's proof of full COVID-19 vaccination mandate, one of the strictest in the United States, went into effect.
Many of the protesters carried American flags and signs decrying vaccination requirements. Few were wearing masks amid the large crowd.
Dozens of people among the crowd were wearing clothes designating their employment with the Los Angeles city and county fire departments, the Los Angeles Department of Water and Power, the Los Angeles County Metropolitan Transportation Authority and other government agencies.
Many people who appeared to be government employees declined to be interviewed, but a few employees said they were prepared to lose their job over the city's vaccination mandate.
Los Angeles firefighter Scott Tomlin said he is prepared to lose his job "because I'm not prepared to lose my life over it."
"The Vaccine Mandate will cause the loss of a highly trained and skilled workforce in Los Angeles," organizers of the rally said in a statement. "This will not only cause pain, suffering and mental anguish to the employees that are to be terminated, it will also deny the protection, safety and city services the residents of this great city have been afforded by their elected officials who have now created this new set of problems."
City News Service contributed to this report.