Serge Gravel was found shot to death on Monday in a hotel room in the coastal town of Jaco.
Reports say authorities in Costa Rica consider the death a possible suicide, but his family in Quebec disputes that claim and wants authorities to launch a full investigation.
Gravel's sister says her 60-year-old brother had three gunshot wounds to the chest.
Foreign Affairs says its thoughts are with the victim's family and a spokeswoman confirmed Canadian officials in Costa Rica are helping the family.
A member of Gravel's family said there would be no further comment for now.