There are several procedural pathways for a party to ask a court to hold that particular entity 'A' has no copyright interest in a work. I can think of four:
- a party 'B' seeking a declaration that it ('B') owns the copyright to the work, rather than 'A' (see e.g. Apotex Inc. v. AstraZeneca Canada Inc.,  4 F.C. 826 (C.A.));
- a party 'B' seeking a declaration of non-infringement with respect to the work (see e.g. Research in Motion Limited v. Atari Inc. (2007) 61 C.P.R. (4th) 193 (Ont. Sup. Ct.));
- in the case where the copyright has been registered, there is an administrative action under s. 57(4) of the Copyright Act, whereby "any interested person" can apply to the Registrar of Copyrights to have an entry expunged from the Register for being "wrongly made"; or
- where party 'B' has been sued by 'A' for infringement, and 'B' is simply arguing that 'A' does not even own the copyright.
In the first three cases, the burden is on the moving party ('B') to establish that 'A' does not own the copyright.
In the fourth case, the burden is on the plaintiff ('A') to establish, as an element of infringement, that they ('A') in fact own the copyright to the work.
As for what evidence could be brought, see: How do you prove a fact at issue in litigation?
If a work has been registered in the Register of Copyrights, the certificate of registration of copyright is "evidence that the copyright subsists and that the person registered is the owner of the copyright." However, this is only evidence, and a court "should rely on these certificates as proof of ... ownership of copyright ... only to the extent that there is no contradictory evidence" (Andrews v. McHale, 2016 FC 624, at para 56).