You can't maintain permanent resident status in Canada if you don't want to pay Canadian taxes. A claim of permanent residence is exactly that, and the CRA consider it a residential tie for tax purposes. Even if you spent all of your time outside of Canada, during the period you claim permanent residence you would have to pay Canadian taxes. (People get too wound up about the 183-day rule, that rule is only relevant in determining residency after everything else has been considered.)
What you would have to do is become a citizen first, then you can maintain your right to reside in Canada and work here but you could also be a non-resident (although that is hard to pull off, the CRA find it hard to believe a Canadian working in Canada is a non-resident for tax purposes, however you can maintain your right to live in Canada while working outside the country and being a tax resident of somewhere else).
Also if you have been filing in Québec for awhile and you switch to being a non-resident filer, the tax people in Québec may not believe you are a non-resident, but you'd have to talk to an accountant familiar with the caselaw in Québec on that one.
Bear in mind if your income comes from Québec you would still pay Québec taxes, because they are higher than the taxes in NC so the foreign tax credit wouldn't cover it all. However from the sounds of it if you route your salary via the US rather than it going via Québec you could get around that. (But you would have to be registered as self-employed in the US, assuming your Canadian employer isn't registered in the US). So yes if you did that, you would only have to pay Québec taxes on your Québec-source income, which would be the rental income from your property there.
BC has the lowest marginal rates of income tax (at least at the lower income levels) however that is misleading because Alberta has no PST and the healthcare premium was recently abolished. Plus property taxes tend to be lower and also natural gas is subsidised. Generally speaking you will pay less tax in Alberta than in BC.
However the lowest tax jurisdictions in Canada are the territories, because you can claim the northern resident deduction and there is no PST up there.
Also bear in mind that if you have US property you could be subject to departure tax, although it's pretty unlikely given the current drop in real estate prices in the US. Have a read of: http://www.cra-arc.gc.ca/tx/nnrsdnts/nd ... n-eng.html


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