But I assum you meant "non-resident for income tax purpose".
To answer your question under three situations:
1) If you've never established your "ties" in Canada and become a resident, you don't have to "apply" to become a non-resident, because you've always been a non-resident. You just don't file tax return if you don't have Canadian source income.
2) If you've established ties in Canada and have been a resident, but cut your ties and become a non-resident during the year, you should indicate this information on your last tax return, but the information is subject to the srutiny of CRA.
3) If you established your ties sometime in the past, then cut them, being a non-resident for a few years, then decide to come back again, you need to start filing as a resident again from the date you establish your ties again. You should indicate this information on your first tax return after you return as a resident.
To answer your question under three situations:
1) If you've never established your "ties" in Canada and become a resident, you don't have to "apply" to become a non-resident, because you've always been a non-resident. You just don't file tax return if you don't have Canadian source income.
2) If you've established ties in Canada and have been a resident, but cut your ties and become a non-resident during the year, you should indicate this information on your last tax return, but the information is subject to the srutiny of CRA.
3) If you established your ties sometime in the past, then cut them, being a non-resident for a few years, then decide to come back again, you need to start filing as a resident again from the date you establish your ties again. You should indicate this information on your first tax return after you return as a resident.