In general, you should only need to complete the medical statement anytime you take a training course. If there are any "yes" answers to the questionnaire your physician will need to sign off approving your diving activities. If you are taking multiple courses through the same instructor & dive center, that physician's approval is good for up to one year.
Each agency has a slightly different medical form but essentially cover the same information. I recommend contacting the dive operator that you will be diving with to verify what they will require. Chances are they have a link to the forms posted on their website in the training section. If you think you might be interested in taking a course of any kind, like Advanced Open Water, or a specialty course like Fish ID or Digital Underwater Photography, you will need a current medical. It can't hurt to travel with it completed, in case you make a spur of the moment decision while on your trip.
I teach in a resort destination and have had divers become interested in taking a specialty class while diving on the boat here, but could not until the had a medical release from their physician back at home.
Have fun and dive safe.