Google has denied the allegations, declaring it had paid all taxes in Indonesia since opening its Jakarta offices in 2011.
The government has repeatedly asserted the California-based company had outstanding tax issues to resolve.
Muhammad Haniv, a senior official with Jakarta's tax office, said Google had refused a request to allow tax officials to examine its financial statements.
"We are now elevating this to an investigation, because they refused to be examined. This could be classified as a criminal offence," Haniv told AFP, adding Google generates tens of millions in advertising revenue but contributed little in tax.
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Global tech businesses have flooded Indonesia in recent years to capitalise on the exploding number of internet users in the Southeast Asian nation, which has an enormous youth population adept at using smartphones.
A third of Indonesia's 255 million have access to the internet but analysts say that number is likely to increase as connectivity improves across the sprawling archipelago.
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