* C$ at C$1.0340 to US$, or 96.71 U.S. cents * Bank of Canada rate decision eyed; move to neutral stance an off-chance * Prices of government bonds fall across the curve By Alastair Sharp TORONTO, May 28 (Reuters) - The Canadian dollar weakened marginally in early trade on Tuesday, as the currency hovered near recent lows ahead of a Bank of Canada rate decision due on Wednesday. The loonie, as Canada's currency is colloquially known, has fallen sharply in recent weeks as domestic data suggests the economy will lag behind its larger neighbor, the United States. "There definitely seems to be a desire to take some exposure to Canada off the table at the moment," said Shaun Osborne, chief currency strategist at TD Securities. At 9:20 a.m. (1320 GMT) the Canadian dollar was trading at C$1.0340 to the greenback, or 96.71 U.S. cents, compared with C$1.0337, or 96.74 U.S. cents, at Monday's North American close. Earlier in May, the loonie had almost breached equal value with the greenback, while several months ago it was worth more than the U.S. dollar as it looked like the Bank of Canada was much more likely to hike rates before the U.S. Federal Reserve. The Canadian central bank is scheduled to make its next rate decision on Wednesday. A Reuters poll shows economists don't expect any tightening until the end of next year as domestic data keeps showing weakness. Some economists have questioned whether the central bank might drop a key phrase about plans to raise borrowing costs eventually. That language makes it the only Group of Seven central bank with an explicit tightening bias. But others have suggested Governor Mark Carney is unlikely to make a policy shift with the last rate announcement before he leaves to head the Bank of England in July. "There is a train of thought in the market that on the basis of the data in Canada there is a justification perhaps for the Bank moving to a neutral stance," Osborne said, adding that a change in policy is not his base assumption. He said the loonie could test C$1.06 within weeks, and that dropping the tightening bias would likely push the currency through C$1.04 on Wednesday. The price of Canadian government debt fell across the curve, with the two-year bond off 2 Canadian cents to yield 1.057 percent, while the benchmark 10-year bond fell 16 Canadian cents to yield 2.000 percent.