GLOBAL MARKETS-Asia shares down before China data, euro hit by Draghi

* China inflation data, RBA quarterly policy statement awaited

* Draghi's hints at near-term ECB steps pressures euro

TOKYO, May 9 (Reuters) - Asian shares got off to a lacklustre start on Friday after a flat performance on Wall Street, with a tense situation in Ukraine adding to the cautious mood ahead of China inflation data later in the day.

The euro was on a shaky footing after tumbling overnight when European Central Bank President Mario Draghi said the central bank might act to stem slowing inflation and boost the euro zone economy.

MSCI's broadest index of Asia-Pacific shares outside Japan was down 0.1 percent in early trading, while Japan's Nikkei stock average shed 0.3 percent.

China inflation data due later on Friday could weigh on markets if it shows an unexpected acceleration in price pressure. On the other hand, a weak rate could equally raise worries about softening domestic demand as the world's second largest economy loses momentum.

Markets were also keeping a wary eye on the Ukraine crisis.

Pro-Moscow separatists in eastern Ukraine ignored Russian President Vladimir Putin's call to postpone a referendum on self-rule, declaring they would go ahead on Sunday with a vote that some fear could lead to war.

U.S. stocks mostly fell on Thursday with the Nasdaq Composite ending lower for a third straight session, its longest losing streak since early April.

But European shares climbed 1.1 percent after ECB's Draghi raised the prospect of action next month to spur the euro zone economy.

The euro came off a 2-1/2 year high against the dollar on Draghi's comments. It was last at $1.3841, steady on the day, and well off Thursday's high of $1.3992, its loftiest peak since November 2011.

As Draghi's dovish comments pushed the euro down 0.4 percent on Thursday against its U.S. counterpart, U.S. Federal Reserve Chair Janet Yellen did the dollar no favours.

Yellen said in testimony to a Senate panel on Thursday that the Fed is in no rush to decide the appropriate size of its balance sheet, but if it ultimately shrinks it to a pre-crisis size, the process could take the better part of a decade.

"In contrast to Mario Draghi, Janet Yellen provided very little clarity on monetary policy this week, keeping the downtrend in yields intact," Kathy Lien, managing director of FX strategy at BK Asset Management, wrote in a note to clients.

The 10-year U.S. Treasury yield was at 2.608 percent, not far from its U.S. close of 2.602 percent on Thursday.

The U.S. dollar index, which tracks the greenback against a basket of six major currencies, eked out a slim 0.1 percent rise to 79.430.

Against the yen, the dollar was steady at 101.63 yen.

In commodities trading, U.S. crude futures were slightly higher at $100.28 a barrel while Brent crude inched lower to $108.00, as traders continued to watch the situation in Ukraine.