The diocese, its bishop and the financial officer are suspected of fraudulently registering thousands of people on its membership lists between 2010 and 2014, which enabled it to obtain 50 million kroner (more than $6.0 million or 5.8 million euros) in state subsidies.
Norway's church denies engaging in fraud but has admitted its past methods were “unsatisfactory.”
In Norway, a predominantly Protestant country, the state provides subsidies to organised religions, the size of which is determined by the number of members.
The Dagbladet daily, which first broke the story, said the diocese had received a letter from the administration on Monday calling for the 40.6 million kroner overpayment to be refunded.
A spokeswoman for the diocese, Lisa Wade, confirmed the contents of the letter. She told AFP that the church would not be paying the sum and would take the matter up with the culture ministry.
"We have a very different understanding of the law,” she said. “It's complex. It's not like it's a clear-cut case.”
Norway's Roman Catholic minority had 140,000 registered members in 2014, more than double the number in 2010.
To explain the jump, the Church has claimed it benefitted from a large wave of Catholic immigrants, notably Poles, who practised their religion but did not register with the Church, which in turn cost the Church more but did not result in increased state subsidies.
Their names have now been removed from the list. More than 21,000 other cases have yet to be clarified. Police raided the Catholic Church's offices on February 26 on suspicions of “aggravated fraud".