CSIS Agents are civilians and have no police power or authority whatsoever. Internal nationals security and intelligence matters used to be handled by the RCMP (which of course do have police powers) however there were a number of instances where RCMP Intelligence Agents were perceived to have abused their police powers so in 1984, the federal government removed responsibility for national security and intelligence from the RCMP's portfolio and created a new civilian agency to handle the work. Thus CSIS was born. If CSIS needs someone arrested or a search warrant executed, the RCMP handle the street level stuff.
CSIS, and their less known counterpart the CSEC, are almost completely focused on internal security. While CSIS certainly has agents working in embassies abroad, there aren't engaged in the covert, deep cover type operations you think of when people say "CIA." Contrary to what you see on television, most of the work carried out by both the CIA and CSIS is done behind a desk and involves reading lots of material and creating intelligence reports.