They will decide - though no country other than Russia is likely to recognise the result - on whether to secede from Ukraine to join Russia. It would be the most significant redrawing of international borders since the Second World War.
Everything would depend on whether Russia's president, Vladimir Putin, uses the vote as an excuse to incorporate the Crimean peninsula into the Russian Federation - if needs be (as in South Ossetia six years ago) by force of arms. The battle for Crimea would be much bloodier and more dangerous for world peace than the five-day war with Georgia in 2008.
Everything in Putin's history, statements and - as far as I can see - psychological make-up suggests he will not shrink from the task.
Make no mistake: Ukraine, and Crimea in particular, are non-negotiable parts of Putin's vision.
For years I have monitored the Russian president's growing paranoia about the West's intentions, and it is clear that events in Ukraine present him with challenges on at least three levels - his own legitimacy as Russian leader, Russia's strategic security, and what he perceives as the interests of Russian citizens living outside the Russian Federation's borders.
To understand Putin's mounting belligerence you have to go back to Ukraine's first attempt to "turn West", in the Orange Revolution of 2004.
By sheer force of numbers, protesters overturned a rigged election that was supported by the Kremlin. One of Putin's advisers, deployed to Ukraine to manipulate the election, described the defeat to me as the start of a "Destroy Russia" project. Another adviser said it was the West's aim to "cause bloodshed" between Russians and Ukrainians. The Kremlin denounced the revolution - which brought a Western-oriented (though utterly inept) government to power - as instigated by and paid for by the United States.
When demonstrators flooded Moscow's own streets in December 2011 to protest against fraudulent parliamentary elections and Putin's decision to return for a third term as president, this too was presented - in Cold War-style television documentaries - as another Western ploy designed to bring down the government. Putin personally accused then US secretary of state Hillary Clinton of "giving the signal" to the protesters.
The ferocity of Putin's comments about such events suggests he is terrified of popular uprisings and foreign interference. It is this fear, more than anything, that explains his constant opposition to Western-sponsored intervention in places such as Libya or Syria. No matter how bad the incumbent leadership, Putin refuses to set the precedent of acquiescing in their removal by foreign intervention.
The last month's events in Ukraine only served to confirm Putin's fears - imaginary or otherwise - about the West's intentions. He saw senator John McCain hobnobbing with the protestors on Kiev's Independence Square and egging them on to bring down the democratically-elected president, Viktor Yanukovych. An intercepted phone call, evidently leaked by Russia's intelligence service, showed the US assistant secretary of state, Victoria Nuland, discussing with the US ambassador which opposition leaders were best suited to which positions in a future Ukrainian government.
It is easy to imagine how livid Putin was at such presumptuousness. The West's instant recognition of the new government was further grist to the mill: for Putin, the nightmare was coming true in front of his eyes.
As he put it in an interview last week: "It is not the first time our Western partners are doing this in Ukraine. I sometimes get the feeling that somewhere across that huge puddle, in America, people sit in a lab and conduct experiments, as if with rats, without actually understanding the consequences of what they are doing."
Rejection of American hegemony in world affairs has been a constant in Putin's stance ever since he came to power. The Kremlin protested impotently when Western nations bombed Kosovo in 1999; Putin criticised the invasion of Iraq (and tried behind the scenes to persuade Saddam Hussein to give up power in order to avoid it); he vigorously protested at the bombing of Libya but failed to stop it; and finally, over Syria, he managed to make the West stop and think.
But when the spectre of Western intervention comes as close to home as Ukraine, Putin will brook nothing at all. For him, this is not just Russia's back yard, it is all but part of Russia itself. "You don't understand, George," he reportedly told president George W Bush in 2008, "that Ukraine is not even a state." On another occasion he referred to Ukraine as "Little Russia", as it was known before the 20th century.
So firm is Putin's conviction that Ukrainians and Russians are blood brothers that he finds it hard to imagine the former might wish to live like Poles or Estonians - nations that threw off their subjugation by Russia and now prosper in the EU and Nato. He either cannot imagine, or does not care, that ordinary Ukrainians are sick and tired of the kleptocratic, corrupt, oligarch-driven government they have in common with Russia. For Putin, it is a given that Ukrainians set their "brotherhood" with Russia above such things. It is a dangerous delusion.
Over the years it seems that Putin has become a man more and more prone to believe his own propaganda. Perhaps he relies too much on his old KGB sources. Unlike his prime minister, Dmitry Medvedev, he does not use the internet, and obtains his information primarily from his advisers, who naturally have an interest in providing him with the kind of facts that he wants to hear. It is perfectly possible that he really believes his secret services' reports about Western intrigues designed to unseat him - and, after all, it is no secret that Western governments openly support opposition groups inside Russia.
So Putin perceives the "struggle for Ukraine" as a prelude to the struggle for the Kremlin. But there is more to his paranoia than that.
Beyond the psychological factors there is Putin's ingrained fear that Nato wants to incorporate Ukraine. For him, this would be the last straw. He would regard himself as failing in the most basic task that falls to any leader - to defend his country's integrity and security. Nato openly courted Ukraine following the Orange Revolution and came close to granting it so-called MAP status - a Membership Action Plan that would have laid the groundwork for eventual membership. Putin was apoplectic, and warned a Nato summit in Bucharest in 2008 that "the appearance on our borders of a powerful military bloc will be considered by Russia as a direct threat to our country's security". As a result, Nato backed away from the plan. But following the overthrow of Yanukovych and Ukraine's renewed attempt to "face west", there is every possibility that Nato will be tempted to revive it.
The danger seen by Putin is not just of a hostile military bloc encroaching on Russia's borders. The Crimea plays host to Russia's Black Sea Fleet, under a leasing arrangement recently extended until 2042. For that to fall under Nato's control would be strategic suicide for Russia - hence the frenetic series of moves since the installation of a Western-friendly government in Kiev last month. The appearance of Russian troops, the blockading of barracks and digging of trenches, the takeover of local government, and the hasty organisation of a referendum - the stealthy annexation of Crimea, in other words - is aimed solely at preventing Russia's warm water base from falling into "enemy" hands in the event of Ukraine deciding to join Nato (even if that, at present, remains a distant prospect).
Putin is as paranoid about Russia's security as he is about his own political future. His fears were fuelled by Washington's development of a missile shield, which Putin believes is aimed at Russia, and by the earlier expansion of Nato into former Warsaw Pact countries - something Nato, according to Russia, pledged never to do.
The final piece in the Putin jigsaw is his presumption that the Kremlin has the right - indeed duty - to protect Russians wherever they may be. After the collapse of the USSR some 25 million Russians found themselves outside the borders of the shrunken Russian state, in newly-independent countries such as Kazakhstan, Estonia and Ukraine.
The new authorities in Kiev made a serious misjudgment in immediately proposing that the use of Russian be banned in Ukraine, even in areas where Russians form a majority and the use of Russian is commonplace in homes and workplaces.
Russian state propaganda jumped on this, and on evidence that the protesters in Kiev and elsewhere included some unsavoury far-right groups, to denounce the entire new government as a band of neo-Nazis, intent on curtailing the freedoms of Russians.
The tactic becomes self-fulfilling: the bloodcurdling propaganda is creating hatred and distrust where there was none. All of this prepares the ground for an eventual Russian invasion of Ukraine "if called upon" by the Russian population. On March 1, Putin signed a decree authorising the use of Russian forces on the territory of Ukraine (a foreign country, let us not forget) "because of the extraordinary situation and threat to the lives of Russian Federation citizens, our countrymen".
No such threat to Russian lives has been evident at all in the days since the pro-Russian government fell, yet the Kremlin seems intent on using the myth as justification for intervention. Sergei Markov, a politician whose views apparently mirror Putin's, seemed to issue an ultimatum, when he wrote last week: "If the junta leaders want to avoid war, they need to adopt Moscow's peaceful and democratic proposals and adhere to them."
He articulated Putin's fear of the revolution spreading to Russia when he added: "Russia's opposition movement will surely want to use the successful experience and technology of the [Kiev] protests and, with the help and financial support of the West, try to carry out their own revolution in Moscow.
"The goal: to remove President Vladimir Putin from power and install a puppet leadership that will sell Russia's strategic interests out to the West in the same way former president Boris Yeltsin did in the 1990s."
All of this is watched with growing fear in other former Soviet republics with sizeable Russian populations. Latvia and Estonia, for example, which are now members of Nato, have been constantly criticised for "violating the rights" of their Russian citizens.
If Crimea votes next week to join Russia, and Putin sends in his troops to "help the Russian population", then what next?