* Canadian dollar weakens 0.3% against the greenback

* Touches its weakest since Dec. 12 at 1.3613

* Canada's annual inflation rate cools to 2.8%

* Bond yields fall across the curve

TORONTO, March 19 (Reuters) - The Canadian dollar weakened to a three-month low against its U.S. counterpart on Tuesday as an unexpected cooling in domestic inflation bolstered expectations the Bank of Canada would begin cutting interest rates in the coming months.

The loonie was trading 0.3% lower at 1.3565 per U.S. dollar, or 73.72 U.S. cents, after touching its weakest intraday level since Dec. 12 at 1.3613.

Canada's inflation rate cooled in February to an annual rate of 2.8%, its slowest pace since June, and closely-watched core inflation measures eased to more than two-year lows.

"The Canadian economy is much weaker than the headline data suggests, and we're now starting to see that weakness manifest within nearly all macro indicators, even the BoC's preferred core measures of inflation that were a major sticking point for the bank back in 2023," said Simon Harvey, head of FX analysis for Monex Europe and Monex Canada.

Money markets see a 75% chance of the BoC easing in June, up from roughly 50% before the data.

"The Bank of Canada is in a tough place," said Darcy Briggs, a portfolio manager at Franklin Templeton Canada.

"The data alone ... it would suggest that the Bank of Canada has a green light to cut rates but they're kind of tethered to Fed policy. And part of that has to do with if they start cutting too soon or by a greater amount then you could have the loonie depreciate quite dramatically."

Investors are concerned that the Federal Reserve will reveal new economic projections on Wednesday that signal fewer interest rate cuts and a later start to the policy easing cycle.

Canadian bond yields fell across the curve. The 2-year was down 12.5 basis points at 4.174% after posting on Monday its highest intraday level in one month at 4.318%. (Reporting by Fergal Smith Editing by Bernadette Baum and Nick Zieminski)