You should direct your query to an experienced Canadian immigration attorney. Having an asylum status in United States will not necessarily diminish your eligibility for status in Canada if you are otherwise eligible for such status. However, I must point out you should consult in depth both with an experienced U.S. immigration lawyer as well. It is unwise to be a U.S. legal resident alien green card and simultaneously hold the similar status in Canada
Answered on Jun 26th, 2014 at 10:07 PM