Most of the rules are in Art 11 of the ANO.
It's worth pointing out that it's not for the owner/operator to decide which he wants. If the a/c is eligible for a C of A it cannot be put on a Permit.
There are a few exceptions that have come about over the years where there has been no Type Certificate Holder to take responsibility for airworthiness and aircraft formerly on a C of A have been allowed to go on a Permit. If the TC is resurrected there is then no route back to a C of A. This can lead to situaitons like the Luscombe where some are on Permits but any new imports would have to go on a C of A.