The way Danes vote will be the crucial influence on money markets today.
Whether Denmark adopts the euro - the European currency unit - is likely to be decided by a handful of voters.
Polls showed there was nothing between those for and against.
The Danish verdict on the euro, expected around 8.30 am, could initially lead to sharp swings in the currency. But financial markets expect the European Central Bank to intervene to support the euro if a "no" vote sparks heavy losses.
Yesterday, the New Zealand dollar closed up at 41.65USc locally, recouping small losses earlier in the day.
Remarks wrongly attributed to European Central Bank President Wim Duisenberg threatened to give the "no" camp a late wave of support, by fanning Danish fears that euro membership might cause welfare cuts.
The ECB, determined to defuse the potential impact on Denmark's four million voters, was quick to deny the comments published in a Swiss magazine, which had indicated the bank would pressure Denmark to reform its pension system.
A "no" would add to downward pressure on the euro, which has depreciated by around 30 per cent against other major currencies since its launch last year.
It would be seen as a vote of no confidence in the currency from one of Europe's most prosperous countries.
Danish rejection would also do little to help the pro-euro camps in Britain and Sweden. Analysts say a "no" could harm European integration by creating a two-speed Europe with the EU's three remaining euro zone "outs" in the slow lane.
Public support has also waned in the 11 countries that adopted the currency in 1999. One recent poll showed 51 per cent of the Dutch were against it, and only 31 per cent in favour.
Cliffhanger Danish vote crucial
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