Canada-US Income Tax Convention have been signed desiring to avoid double taxation.
In the case of Canada, if you pay income tax to the United States for the income earned in that country, you can claim foreign tax credits against that income in Canada. Foreign tax credits include federal income tax, state income tax, social security taxes etc.
In the case of the United States, if you pay income tax to Canada with respect to the income earned in that country, you can claim foreign tax credits or foreign earned income exclusion or a combination thereof. Although foreign tax credits and foreign earned income exclusion are available at the federal level, this may not be true at the state level. Some states such as California and New Jersey may not honor tax treaties between Canada and the United States i.e. the income tax paid to the province of Canada may not be available for foreign tax credits when calculating tax liability for these states. Accordingly, some double taxation may happen at state level.