Territorial limit is 12 NM not 3. Changed a long time ago.
Limited control out to 70 NM (pollution control) and Economic
explotation (minerals and fish) to 200 NM.

Right to stop and search a ship is restricted.
If the vessel is owned by a government the US is not allowed to
search it; even if within US territorial limits. The most they
can do is demand that the ship leave US waters (weather and
seaworthyness permitting).

However, they do have the right to stop and search a ship if it is headed
for a US port.

Tom Smith