The Spanish-speaking US territory's referendum proposes "the immediate decolonisation of Puerto Rico" - just as the bankrupt island is drowning in USD 70 billion in debt.
Its young governor, Ricardo Rossello, said that regardless of the crisis the referendum could not wait, repeating over the past several days in interviews and on Twitter that "the moment to vote for the decolonization has arrived!"
But the opposition Popular Democratic Party, which favors the status quo, sought on Sunday to play down the eventual results.
The boycott would seem to give an edge to voters favoring statehood, which the new government insists is the answer to the financial crisis hanging over the island of 3.4 million.
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"I want to guarantee the future of my children and my grandchildren with the federal contributions" that statehood would bring, housewife Miriam Cruz told AFP after casting her vote.
Polls opened at 08H00 local (12H00 GMT), under an atmosphere of skepticism: opposition parties had not campaigned, there were no political caravans exhorting people to vote, and turnout appeared to be light.
He came to power in January on the promise that he would work to end a long "colonial" relationship with the United States and make the island the 51st state.
The question of status is "fundamental" to breaking free from economic turmoil, said Christian Sobrino, chief economic advisor to the government.
"It is because Puerto Rico is in an unequal relationship" with the US government that the bankrupt island's finances are now under a largely US-appointed control board, he told AFP.
A former Spanish colony taken over by the US at the end of the 19th century, Puerto Rico has enjoyed broad political autonomy since 1952 as a commonwealth or "free associated state."
Many Puerto Ricans attribute the malaise plaguing the island to Washington's power over them.
For decades the territory enjoyed a US federal tax exemption that attracted many American companies to set up shop - but those breaks were ended in 2006, prompting firms to leave the island en masse.