Canada geese mate for life. The living mate will probably stay close to the body for awhile. It will leave when it is ready.
If possible, leave the body of the dead goose where it is at overnight. There are many species of wildlife that would potentially take the goose. If it is still there tomorrow, and if it is causing a concern because of children or pets in the neighborhood being around it, call Public Works to see if someone will come pick up the goose. (309) 434-2225