I asked same question here before

We had problem when we landed in Canada. On US border, if officer asks you whether you apply US GC, you will have problem. If answer no, you are lying. If answer yes, they will put notes saying you already have Canada PR so you are not qualify for US GC. They did this thing to us. I don't know what will happen later. Somebody said we will have choice to pick one country when we reach some point for example, GC interview. But I don't know it will happen or not. I hope somebody can give us a clear answer, by law, can a Canada PR apply US GC?