to issue an injunction, writ of certiorari, writ of prohibition, writ of mandamus or writ of quo warranto, or grant declaratory relief, against any federal board, commission or other tribunal.A notable absentee from this list is the writ of habeas corpus. Since its assertion that the "rule of law must run within penitentiary walls", the Supreme Court of Canada has given prisoners a choice between making habeas claims in the provincial superior courts or judicial review applications in Federal Court.
As explained in May v. Ferndale Institution,  3 S.C.R. 809:
44 To sum up therefore, the jurisprudence of this Court establishes that prisoners may choose to challenge the legality of a decision affecting their residual liberty either in a provincial superior court by way of habeas corpus or in the Federal Court by way of judicial review. As a matter of principle, a provincial superior court should exercise its jurisdiction when it is requested to do so. Habeas corpus jurisdiction should not be declined merely because another alternative remedy exists and would appear as or more convenient in the eyes of the court. The option belongs to the applicant. Only in limited circumstances will it be appropriate for a provincial superior court to decline to exercise its habeas corpus jurisdiction. For instance, in criminal law, where a statute confers jurisdiction on a court of appeal to correct the errors of a lower court and release the applicant if need be, habeas corpus will not be available (i.e. Gamble). Jurisdiction should also be declined where there is in place a complete, comprehensive and expert procedure for review of an administrative decision (i.e. Pringle and Peiroo).Given the place of habeas in the common law tradition, this conclusion is hardly surprising. The Court also emphasized that certiorari could also be sought "in aid" of a habeas application in a provincial court.
Nonetheless, it can be said that a prisoner challenging the substantive reasonableness of a decision to classify him or her as a minimum- or maximum security detainee is really asking for the classification decision to be quashed, not to be released from custody and that accordingly, he or she should knock on the door of the Federal Court.
This argument failed in Mission Institution v. Khela, 2014 SCC 24, a case which may have removed another potential barrier to access to the provincial superior courts. (I say "may" because the case was ultimately resolved on procedural fairness grounds similar to those at issue in May, so the disclaimer applies that any additional discussion may have been obiter!)
Prior to Khela, it was clear that jurisdictional errors and breaches of procedural fairness entitled an individual to habeas corpus. But as administrative law has moved on, habeas has not quite moved in lockstep. Khela moves it forward.
Administrative lawyers in Canada do not really talk about jurisdiction any more. "Standard of review" is really all that matters. A decision that does not survive scrutiny for correctness or reasonableness is unlawful and, as LeBel J. explained, cannot justify the continued detention of a prisoner:
Beneath the discussion of habeas and competing jurisdictions, then, lies a useful description of the modern law of judicial review. The above reasoning leads to the conclusion that an inmate may challenge the reasonableness of his or her deprivation of liberty by means of an application for habeas corpus. Ultimately, then, where a deprivation of liberty results from a federal administrative decision, that decision can be subject to either of two forms of review, and the inmate may choose the forum he or she prefers. An inmate can choose either to challenge the reasonableness of the decision by applying for judicial review under s. 18 of the FCA or to have the decision reviewed for reasonableness by means of an application for habeas corpus. “Reasonableness” is therefore a “legitimate ground” upon which to question the legality of a deprivation of liberty in an application for habeas corpus.
There is also a useful description of what reasonableness review might entail in this context:
Whether and to what extent this description can be accommodated in the emerging concept of the flexible "range" of reasonable outcomes or requires an additional distinction between the "range" for legal questions and the "range" for factual ones is a question for another day (though regular readers will appreciate that my answer is likely to be in the negative!). As things stand, a decision will be unreasonable, and therefore unlawful, if an inmate’s liberty interests are sacrificed absent any evidence or on the basis of unreliable or irrelevant evidence, or evidence that cannot support the conclusion, although I do not foreclose the possibility that it may also be unreasonable on other grounds. Deference will be shown to a determination that evidence is reliable, but the authorities will nonetheless have to explain that determination.