* C$ at C$1.0044 vs US$, or 99.56 U.S. cents * Strongest close vs greenback since Feb. 14 * Global stock markets hit highest levels in five years * C$ surges against Aussie as RBA cuts rates * Bond prices lower across the curve By Alastair Sharp TORONTO, May 7 (Reuters) - The Canadian dollar closed at its strongest level versus its U.S. counterpart since mid-February on Tuesday, rising with stock markets around the world in a risk rally fueled by signals that top central banks will keep supporting economic growth. The Canadian currency also gained sharply against its commodity-backed cousin in Australia after that country's central bank cut interest rates. Mark Chandler, head of Canadian fixed income and currency strategy at Royal Bank of Canada, said the Australian rate cut and the Canadian dollar's subsequent rally against the Aussie showed investors are more willing to bet on growth in Canada's biggest export market, the United States, than on a soft landing in Australia's biggest commodity customer, China. "There is a bigger story developing this year," Chandler said. "The nod went to Australia throughout much of the last few years," he said, referring to the Australian currency outperforming Canada's in that period, due in part to strong Chinese demand for Australia's resources, compared with slower U.S. consumption of Canadian commodities. MSCI's global index, which tracks stocks in 45 countries, edged past its June 2008 highs in Asian trading on Tuesday with Japan's Nikkei stock index jumping in a delayed reaction to Friday's U.S. jobs data. The Tokyo market was closed on Monday. The momentum continued in Europe, where the DAX hit a record following strong industrial data. The head of the European Central Bank underpinned the positive mood on Monday by saying the ECB was ready to trim interest rates again if needed, while the Reserve Bank of Australia cut rates to a new low of 2.75 percent on Tuesday and suggested it may do more. "The Canadian dollar is being held up by some of the crosses, particularly the Aussie-CAD ... in the backwash of the RBA move, and that has provided a reasonably healthy backdrop for the Canadian dollar overall," said Jeremy Stretch, head of foreign exchange strategy at CIBC World Markets in London. The Canadian dollar ended the day at C$1.0044 to the U.S. dollar, or 99.56 U.S. cents, its strongest close since Feb. 14 and up from Monday's North American close of C$1.0068 to the U.S. dollar, or 99.32 U.S. cents. The Canadian dollar rallied to its strongest level since October against Australia's currency after the RBA surprised many traders with the rate cut. The Canadian dollar firmed as far as C$1.0204 to the Australian currency. Stretch said traders would be watching data on Canadian housing starts, due to be released on Wednesday. The report is expected to show the pace of new homebuilding slowed to a seasonally adjusted annual rate of 175,000 units in April, down from 184,000 units in March. Investors were also awaiting Friday's Canadian employment data. The report is expected to show the economy added 15,000 jobs in April, while the unemployment rate held steady at 7.2 percent, according to a Reuters survey of analysts. RBC's Chandler said he expects a decent jobs report could push the Canadian currency through the psychologically important one-to-one level with the U.S. dollar. Traders are also looking for more clues on what newly appointed Bank of Canada Governor Stephen Poloz will say about monetary policy. Prices for Canadian government bonds were lower across the curve. The two-year bond fell half a Canadian cent to yield 0.979 percent, while the benchmark 10-year bond fell 19 Canadian cents to yield 1.822 percent.