The Men in Black organisation operates in America, we establish that for sure. The films all are based in America also. What I would like to know is whether there are any boundaries upon the Men in Black organisation i.e. are they focused just in America (which I doubt) or do we see evidence somewhere of agents operating outside of America?
MIB are indeed international. From the script:
(Men in Black headquarters) ON THE MAIN FLOOR, they walk briskly across the room, reaching a giant screen on the far wall.
KAY: Observation, the heart of our little endeavor.
The screen displays a map of the world on which thousands of tiny lights blink in all parts of the globe, log lines of data flashing next to them.
KAY: This map shows the location of every registered alien on Earth at any given time. Some of them we keep under constant surveillance.
There is more, like the leather-bound book entitled "Active on Earth" Jay receives after signing up.
Additionally, in Men In Black II, we saw an agent in Antarctica on the massive screen. The agent states "Zed, the Treaty is Signed", meaning MIB likely has at least some international juristiction.