The notification bar asking to vote for so community moderator re-appears on every page refresh and I have voted already. I couldn't find any submit buttons, but is there some other action I need to perform besides selecting my first, second and third candidates?
Do you mean the system message?
If so this gets displayed for as long as it's active - either for 48 hours or until a moderator removes it.
If you mean the notification that pops down then if you click the "X" and refresh the page then it won't get shown again.
Neither message "knows" whether you have voted or not.