City officials revealed last Thursday that Balderrama admitted in February to an "inappropriate off-duty relationship he was involved in with a non-city employee."
Action News has now confirmed leaders of the Fresno Police Officers Association raised questions about the investigation in a message to union members on Friday.
"There has also been a prevalent narrative surrounding this situation that no policy violations have been established," Board President Brandon Wiemiller wrote.
"This is an incredible offense to every sworn member of the agency, who is held to account for policy violations surrounding "discretion" and "conduct unbecoming."
Union leaders are now calling an emergency board meeting on Wednesday as questions mount for the leader of nearly 900 police officers in California's fifth-largest city.
It is unclear why Balderrama is allowed to stay in his position or why he came forward in February.
Asked for more information on Monday, the mayor and city managers's representative said they had "no further comment."
Balderrama has stayed away from reporters. Instead, the chief is posting scripture and department news on social media.
Criticism of Balderrama comes as Action News has confirmed part of the police department's internal policy.
A portion states that employees could face disciplinary action for on or off-duty conduct that is unbecoming or reflects unfavorably on the department or its members.
City Attorney Andrew Janz said late Monday that the investigation into Balderrama is ongoing and will be "thorough."
City officials will review the final report confidentially, Janz said.
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