Can an application for permanent residence be refused at the federal level, after the applicant has obtained a CSQ?

Yes. An application can be refused at the federal processing stage for a variety of reasons. The decision to refuse an application at the federal level can be based on criminal background checks, or on the results of medical examinations. An application may also be refused if the federal immigration authorities have reason to believe any of the applicant's claims on their application are untrue, or if the authorities doubt the applicant's intention to reside in Quebec.