Assuming you're a PR in Canada, you'd have to file returns for both the U.S. and Canada.
There is a tax treaty between Canada and the U.S. that states you should not have to pay more taxes to both countries than you would have to one of them. So you file your U.S. federal and state returns, and then the Canadian returns with a tax credit for taxes you paid to the U.S. The result is that you pay an amount equal to just the Canadian taxes - but it's split.