In NH, county government is fairly weak - most of the power resides at the city/town or state level. One thing the counties do is to run the court system. Sheriffs in NH do mostly court-related work - prisoner transport, security for the courts, some delivery of writs, etc. They also can backup the local or state police if needed. They also provide most of the LEO work at the airports -- you'll see they back up the federal screeners at Manchester Airport for example.

--pete

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2004 330xi, 2002 K1200RS