You do not cease to be a resident of Canada simply because you have an active green card. It is entirely possible to be considered a resident by both countries since they have different rules.
From the US viewpoint, all citizens and green card holders are considered residents for tax purposes, regardless of where they live, even if they have never even visited the US. This comes with certain benefits, as well as certain obligations (notably taxes).
From a Canadian viewpoint, you are deemed a resident, or not, based on a variety of other factors, including physical presence, family, work, house ownership, etc. A US green card can be a factor which tips the scale toward being a non-resident in Canada, but of itself, it is not conclusive. You remain a dual resident until your residential ties become stronger in US than they are in Canada.
I have heard much discussion to the contrary, so I submitted the official paperwork to the Canadian government for them to make a determination on my residency. They determined that in my case, the green card alone was not sufficient to deem me a non-resident in Canada. I would like to hear other official determinations on such matters for similar cases.