* Investors jittery after proposal to tax Cypriot deposits * Euro falls broadly, hits 3-month low vs dollar * Focus on Cyprus parliament vote, peripheral bond yields By Nia Williams LONDON, March 18 (Reuters) - The euro slumped on Monday as investors took news of a bailout plan for Cyprus that involves taxing bank deposits as a dangerous precedent that could ultimately lead to bank runs elsewhere in the euro zone. Euro zone finance ministers demanded at the weekend that Cypriots pay up to 9.9 percent of their deposits in exchange for a 10 billion euro ($13 billion) bailout. The move broke with previous EU protocol that citizens' savings are sacrosanct and led to worried Cypriots emptying cash machines on the island as they rushed to access their funds. Cyprus's parliament will vote on the plan on Monday, with growing speculation the tax on deposits below 100,000 euros might be lowered to lessen the blow for smaller savers. Analysts said the vote should offer some clarity and help limit further losses in the euro for now, but the single currency would remain vulnerable. "If this tax is levied it will set a precedent. It raises questions over whether other deposits will be safeguarded in other countries," said Jane Foley, senior currency strategist at Rabobank. "Euro zone politicians will be at pains today to manage down the danger of contagion to other (peripheral) markets. The euro will find a little bit of support from that but markets will remain jittery." The single currency dropped to a three-month low of $1.2882, before paring losses to last trade down 0.8 percent on the day at $1.2965. Against the yen, the euro tumbled as mush as 2.1 percent, briefly breaking through support at 121.681, its 55-day moving average. It was last down 1.1 percent at 123.07 yen . The euro also fell 0.5 percent against the Swiss franc to 1.2213 francs and 0.9 percent against the British pound to 85.64 pence. "It was a big shock to hear that they will tax savings, and the worry is that this could impact larger countries like Spain or Italy," said Kenichi Asada, manager of forex at Trust & Custody Services Bank. Market players will keep a close watch on peripheral euro zone bond spreads for signs of contagion from Cyprus. YEN CHOPPY The yen shot higher across the board as speculative sellers were caught short of the currency, and had to unwind positions. The highly liquid Japanese currency is considered a safe haven by many investors and tends to rise in times of market stress. The dollar dropped to as low as 93.45 yen in volatile early trade, its lowest since March 6 and moving away from a 3-1/2 year peak of 96.71 struck on March 12. It was last down 0.4 percent at 94.87 yen. Some strategists said the yen's strength would be short-lived given bets on more aggressive easing steps from the Bank of Japan, and expectations that euro zone politicians will be able to reassure markets. "It's short-term negative for risk, the euro and dollar/yen but we think it shouldn't last too long ... The broad trend for yen weakness is still intact despite the near-term upside," said Bill Diviney, currency strategist at Barclays in Tokyo. "Our view is that ultimately the backstops are in place to prevent any more contagion. The ECB's policies and also banks are in a much better position than they were last year." The U.S. dollar rose 0.4 percent against a basket of currencies to 82.603. An improving U.S. economy has underpinned the dollar in recent weeks. Data released on Friday showed U.S. manufacturing was growing, although consumer sentiment in the world's biggest economy faltered to its weakest in over a year and inflation picked up.