* Canadian dollar at C$1.3305 or 75.16 U.S. cents
* Canada's annual inflation rate cools to 1.3 percent in May
* Bond prices higher across much of a steeper yield curve
* Two-year yield falls 3 basis points further below its U.S. equivalent
By Fergal Smith
TORONTO, June 23 (Reuters) - The Canadian dollar fell on Friday against its U.S. counterpart after weaker-than-expected domestic inflation data reduced the chances of an interest rate hike next month from the Bank of Canada.
The annual inflation rate cooled to 1.3 percent in May, below forecasts for 1.5 percent, pushing it further away from the Bank of Canada's 2 percent target as the cost of food fell and gasoline prices moderated, data from Statistics Canada showed. central bank's three measures of core inflation remained subdued.
"It is going to be very difficult for the Bank (of Canada) to hike as soon as next month when you still haven't carved out a bottom on inflation," said Derek Holt, head of capital markets economics at Scotiabank.
Chances of a hike in July fell to just 20 percent from one-in-three before the inflation report, data from the overnight index swaps market showed. BOCWATCH
The Bank of Canada's top two officials last week said that looser monetary policies put in place in 2015 had largely done their work, and the bank would assess whether rates must remain at near-record lows. 9:13 a.m. ET (1313 GMT), the Canadian dollar CAD=D4 was trading at C$1.3305 to the greenback, or 75.16 U.S. cents, down 0.5 percent.
The currency traded in a range of C$1.3211 to C$1.3307.
Canadian government bond prices were higher across much of a steeper yield curve, with the two-year CA2YT=RR price up 4.5 Canadian cents to yield 0.911 percent and the 10-year CA10YT=RR rising 10 Canadian cents to yield 1.489 percent.
The two-year yield fell 3 basis points further below its U.S. equivalent to a spread of -43.8 basis points, as Canadian bonds outperformed. On Thursday, the spread had touched its narrowest in nearly four months at -40.8 basis points.