* Canadian dollar falls 0.2% against the greenback

* Touches a one-week low at 1.3675

* Canada's annual inflation rate slows to 2.7%

* 10-year yield eases 4.9 basis points to 3.576%

TORONTO, May 21 (Reuters) - The Canadian dollar weakened to a one-week low against its U.S. counterpart on Tuesday as investors priced in a greater than evens chance the Bank of Canada would cut interest rates in June after domestic data that showed further cooling of inflation.

Canada's annual inflation rate slowed to a three-year low of 2.7% in April, matching estimates, and core measures continued to ease.

"Swap-implied odds on a Bank of Canada rate cut at the June meeting are rising beyond the 50-percent threshold, sending the Canadian dollar sharply lower against the greenback," Karl Schamotta, chief market strategist at Corpay, said in a note.

Investors see a 56% chance that the BoC would begin a rate cutting campaign at its next policy decision on June 5, up from roughly 40% before the inflation data, swaps market data showed.

"It is clear that economic downside risks should now outweigh inflation in determining policy settings. The Canadian dollar could remain under selling pressure until the U.S. joins the country in exhibiting signs of a slowdown," Schamotta said.

The BoC would be willing to cut interest rates three times ahead of the Federal Reserve's first move before a declining currency threatens to endanger the inflation outlook, the median estimate of seven analysts in a straw poll showed.

The Canadian dollar was trading 0.2% lower at 1.3650 to the U.S. dollar, or 73.26 U.S. cents, after touching its weakest intraday level since last Tuesday at 1.3675.

Adding to headwinds for the Canadian currency, the price of oil settled 0.7% lower at $79.26 a barrel. Oil is one of Canada's major exports.

Canadian bond yields moved lower across the curve. The 10-year was down 4.9 basis points at 3.576%, while it was trading 2.8 basis points further below the U.S. equivalent at a spread of 84 basis points. (Reporting by Fergal Smith; editing by Jonathan Oatis and Alistair Bell)