* Canadian dollar weakens 0.3% against the greenback

* Canadian services PMI shows activity slowing

* Price of U.S. oil falls 1%

* 10-year yield hits a 4-1/2-month low

TORONTO, Dec 5 (Reuters) - The Canadian dollar weakened against its U.S. counterpart on Tuesday as the greenback notched broad-based gains and domestic purchasing mangers' index (PMI) data showed the downturn in the services sector deepening in November.

The loonie was trading 0.3% lower at 1.3575 to the greenback, or 73.66 U.S. cents, after moving in a range of 1.3535 to 1.3591. On Monday, it touched its strongest intraday level in two months at 1.3477.

The decline for the loonie comes "as gold's blow-off top yesterday encourages some broad USD buying, oil and copper selling to come back in," said Erik Bregar, director, FX & precious metals risk management at Silver Gold Bull.

Gold extended its pull-back from an all-time high it posted on Monday, while the price of oil, one of Canada's major exports, was down 1% at $72.31 a barrel and the U.S. dollar rallied against a basket of major currencies.

The S&P Global Canada Services Business Activity Index fell to 44.5 in November from 46.6 in October, its lowest level since June 2020, pressured by increased borrowing costs and worries about a potential recession.

Signs of an economic slowdown are expected to keep the Bank of Canada on hold at a policy announcement on Wednesday, after the central bank raised its benchmark interest rate to a 22-year high of 5% in July.

Economists polled by Reuters expect the BoC to start cutting rates in the second quarter and forecast borrowing costs will drop by at least one percentage point by the end of 2024.

Canadian government bond yields were lower across the curve, tracking moves in U.S. Treasuries after U.S. data indicated the labor market was easing.

The 10-year was down 8.7 basis points at 3.362%, after earlier touching its lowest level since July 19 at 3.342%. (Reporting by Fergal Smith; Editing by Alexander Smith)