Some interesting points raised here about the role of these cutters...........therefore would I be correct in assuming that to distinguish these government department ships from military ships........they carry no arms whatsoever?........even small arms?
Many Coast Guard Cutters are armed. With drug lords, or with interdiction within your own waters, be it port security, or coast line, or inland waterways there is the danger of armed adversaries and so a cutter must be able to defend itself...or take the fight to the vessel that is intruding.
The large US Coast Guard Cutters, called National Security Cutters have a 57mm main gun and a 20mm CIWS and are capable of adding an Mk-41 VKS. The Offshore Patrol Cutters will also have a 57 mm main gun. The next smaller size carries a 25mm chain gun. Other cutters are armed with 20mm guns, and then mounted .50 caliber guns. All of them have small arms.
USCG Legend Class, National Security Cutter, 4,500 tons, 418 ft long, 3 in service, 8 planned
USCG Offshore Patrol Cutter, 3,000 tons (app.), 350 ft long (app.), 0 in service, 25 planned
USCG Sentinel Class, Fast Response Cutter, 350 tons, 155 ft long, 4 in service, 58 planned
USCG Island Class, Patrol Cutter, 168 tons, 110 ft. long, 41 in service
USCG Protector Class, Coastal Patrol Cutter, 90 tons, 87 ft. long, 73 in service
So it is not an issue of them being unarmed. It is an issue of the role.
Generally in international waters, where either other nations, or large armed non-nation organizations (like large Pirates operations, or Al Quida, etc.) are involved, you will find the military dealing with the issue. In your own territorial waters with small scale piracy, durg lords, criminals and the like, you will find the Coast Guard involved. Now, if a military from another nation comes into your territorial waters with any kind of ill intent...then the Coast Guard may help, but it will probably immediately or quickly escalate to involve the military.