Ford told reporters on Monday that he had received a threat that demanded he resign his post or a bomb would explode at city hall. Police later said they found no evidence of any explosive devices.
The union's grievance against the City of Toronto accuses the mayor of ignoring corporate policy that outlines the appropriate line of communication in case of a security threat or suspicious package.
The president of Local 79 of the Canadian Union of Public Employees said Ford's decision to talk to the media could have caused "chaos and pandemonium."
"It's important to react seriously and to react calmly and thoughtfully but not to be irresponsible like this," Tim Maguire said in a news conference.
"Policies are in place so that people are kept calm, that a threat is investigated."
Speaking to reporters at the opening of the Canadian National Exhibition, Ford said when he learned of the threat, he called security and did what he was told.
"And they said 'We're going to call the police.' I talked to the police. They came into my office," he said.
The mayor said that when he asked police if he should talk to the media the response was "Yes. Do exactly that. We'll follow up."
"They told me what to do and I did exactly what they said," Ford said.
A Toronto police spokesman, however, disputed the mayor's version of events.
"If, as we have been told, the mayor is saying police advised him to discuss the matter with the media, the officers' recollection is different," Victor Kwong said in an email to The Canadian Press.
The union is asking the Ontario Ministry of Labour to investigate, but it's unclear whether the mayor, as an elected official, is held to the same standards as city employees.
Maguire said some city workers first became aware of the bomb threat through media reports.
"Then they were wondering what to do," he said, adding that some people left the building after speaking with their supervisors.
He said the proper line of communication would involve informing police and city management to ensure a calm response.
Maguire cited the provincial Occupational Health and Safety Act, which outlines workplace rights under the Ministry of Labour.
He said everyone in the vicinity of the bomb threat had ``the entitlement to a greater respect than the irresponsibility with which this was treated.''
Maguire said the union is asking the ministry to weigh in on whether Ford technically breached policy.
"We think both city officials and the mayor are responsible to react calmly," he said.
Maguire said he also wants to ensure that those who issue bomb threats aren't emboldened by publicity, and his goal is to prevent a similar chain of events in the future.
"Let's make sure going forward that if there are threats, it's dealt with in a rational manner under the policy, so people's health and safety is looked at," he said.
- With files from Ethan Lou.