Under subsection 126(14) of the EI Act , Service Canada has the lawful authority to request information on current or former employees as it relates to past, present or future EI claims. As an employer, you have an obligation to answer these requests. You are not obligated to inform your employees that you are providing this information. 
Service Canada is not an investigatory body and will only require information used for making an EI claim.
Subsection 7(3) of the Personal Information Protection and Electronic Documents Act (PIPEDA) allows an employer to disclose personal information without the knowledge or consent of the individual if the disclosure is made to a government institution that has identified its lawful authority, and if it is for the purpose of enforcing any law of Canada.