The Professional Institute of the Public Service of Canada is citing a case involving New Brunswick's J.D. Irving Ltd.
The individual background checks are among new security screening standards the Treasury Board says are required to ensure the reliability and trustworthiness of civil servants handling sensitive and personal information.
The new background checks apply to existing employees as well as to new hires.
The Professional Institute of the Public Service of Canada has applied for an injunction to the federal court to halt the added security screening until a full legal challenge can be dealt with.
"We simply have no evidence from the government that such a broad, blanket application is reasonable in any way," said Isabelle Roy, the general counsel for the union, which represents 55,000 civil servants.
"We're simply not convinced of the rationale and reasonability for such privacy invasive measures being implemented across the board."
Roy says the application for an injunction cites the 2013 Supreme Court of Canada case CEP Local 30 v Irving Pulp and Paper.
In that case the top court ruled that privacy rights trump the rights of the company to initiate random alcohol testing on all employees.
'Unwarranted violation of personal privacy'
Another union, the Public Service Alliance of Canada, says it also is challenging the credit check requirement.
"These checks will be an unwarranted violation of personal privacy," said Chris Aylward, the union`s vice president, in a statement to CBC.
"They could put people's livelihoods in jeopardy without cause."
The attempt is also being followed closely by the Canadian Civil Liberties Association.
"Many of these things such as fingerprints - biometrics - are potentially deeply privacy invasive. We think of fingerprints as something we do to criminals not employees in general," said Brenda McPhail, who heads the association's privacy, technology and surveillance project.
"It's going to create an atmosphere in the workplace that suggests as an employer we do not trust you."
Employees will be required to consent in writing to the added security screening. Those who withhold consent will lose their jobs.
Michael Gosselin, a Treasury Board spokesperson, defended the decision in an email statement.
"Canadians have a right to expect that government employees and contractors undergo appropriate security screening which is a fundamental practice before being entrusted with public resources, or with the personal and/or sensitive information they provide when filing their tax return, applying for Employment Insurance, Canada Pension Disability benefits or a passport," he wrote.
The new measures were declared last October.
All federal departments and agencies have been given 36 months to fully comply with the new rule.