"The Bank of Canada is a special type of Crown corporation, owned by the federal government, but with considerable independence to carry out its responsibilities."
https://www.bankofcanada.ca/about
They also add: "The Governor and Senior Deputy Governor are appointed by the Bank's Board of Directors (with the approval of Cabinet), not by the federal government."
... and the BoD are appointed by cabinet.
Does the political branch make the decisions? No. But they choose the people that do!