Last year, editors at the country's Dagens Naeringsliv (DN) newspaper published a story alleging streaming data was manipulated, resulting in the overpayment of royalties for Kanye's "The Life of Pablo" and Jay's wife Beyonce's 2016 record "Lemonade".
Executives at the firm have denied the claims, but Norwegian prosecutors have now confirmed they have opened a criminal probe into the matter.
Elisabeth Harbo-Lervik, the Chief Public Prosecutor at Norway's National Authority for Investigation and Prosecution of Economic and Environmental Crime (Okokrim) confirmed an investigation is underway, telling DN it is "still in its early stages."
DN claim four former Tidal employees, including a Head of Business Intelligence at the Sweden-based firm, have been interrogated by prosecutors so far. Elisabeth also said executives at the premium music streaming service were yet to provide her with all the information she required.
The company's lawyer, Fredrik Berg told WENN that the firm was "not a suspect" and added, "We are communicating with Okokrim. We are aware that at least one person we suspected of theft has been questioned."
Jay, real name Shawn Carter, part-owns Tidal and relaunched it in 2015 with a star-studded event in New York City. Kanye, who is an old friend of the "Hard Knock Life" rapper, and Beyonce debuted exclusively on the service the following year.
Researchers from the Norwegian University of Science and Technology studied streaming information obtained by DN editors from two months in 2016 to see if it tallied with payments of $2.5 million (£1.8 million) and $3 million (£2.2 million) made to the pair's respective record labels, sums they claim were excessive.
Responding to the initial DN story, Tidal chief Richard Sanders called the allegations "false" but said the company had appointed a cyber-security firm to, "further protect the security and integrity of our data."