Hitching on Saint Martin/Sint Maarten island is certainly possible. Sint maarten is very small, and doesn't have any real custom to hitch-hiking, but in spite of that, hitch-hiking is certainly doable. The Island's nickname is The Friendly Island, and the people are indeed very friendly! So if you hitch-hike on St.Maarten/St.Martin, don't expect to get a ride fast (as people are not used to it), but wait a little, and wait for that one cool person who will take you. The conversations are really nice, and the local experience is very worth it. The major advantage on St.Maarten/Martin is that the island is very small, so once you have a ride, you will cover the most of your distance in one ride.
Taxi's are everywhere on St.Maarten/Martin, and it's really easy to get from one place to another on the island. The distinction between taxi and normal passenger car is very small though, so people will often stop for you and ask money for a ride. Keep this in mind.
St.Maarten/Martin has a population of about 75,000 people, on an area of about 85m2. It means a high population density, and therefore a lot of traffic on the roads. St.Maarten/Martin has a slight problem of overcrowding, but for hitch-hiking, this is a good thing :)
St.Maarten/Martin's population is made of a lot of different peoples and nationalities. Most of them are native creoles, born on the island or on neighbouring islands. But there are also large groups of Latin American, North American (USA), and European (French, Dutch) people. In general, North Americans and Europeans are more familiar with hitch-hiking, so they are a good source of rides too.
Where to start
Although you can start just about everywhere on the island, The best places to start is at transportation hubs, like bus stations, airports (St.Maarten/Martin has 2), and the exit lanes out of the 'cities'. A lot of cars depart from there in the same direction.