The Wiki gives a definition as:
A gendarmerie or gendarmery is in principle a military force charged with police duties among civilian populations. Members of such a force are typically called "gendarmes". The Shorter Oxford English Dictionary describes a gendarme as "a soldier who is employed on police duties" and a "gendarmery, -erie" as "gendarmes as a body".
Link:http://en.wikipedia.org/wiki/Gendarmerie

Later it says:
In comparison to civilian police forces, gendarmeries may provide a more disciplined force whose military capabilities make them more capable of dealing with armed groups and with all types of violence.
Generally they are national bodies, which historically have been for internal defence - of the state against threats and not with responsibility for the breadth of roles normally associated with civilian law enforcement. The emphasis is on group action, so they are often based on a company equivalent; in many places working away from their homes.

In Western Europe their responsibilities are now far wider, especially when internal defence has declined and public disorder is now irregular.

I cannot think of any US LE body being like a Gendarmerie.