It depends. :)

If you are not Canadian resident for tax purpose, you don't have to pay Canadian income tax. In order to do that, you have to cut tie to Canada. That is, no residence(house, apartment), immidiate family(spouse, children), bank account, driver's license, medicare card, credit card, etc in Canada. Otherwise, you have to pay Canadian income tax in addition to US tax. Of course, the income tax you pay in US usually is considered as credit when you calculate your Canadian income tax so you are not really paying twice.