The discussion of the Coast Guards in various places and particularly of the USCG has led me to wonder what typical system wide rescue and system LE/security might look like.

I would assume that such a thing might start to exist once you'd been spacing for a while and could get out to the various planets and belts and so on with some ease enough to see some populations out there regularly and on a sustainable basis.

So such an entity might start to be relevant around TL-9, but TL-10 would likely be where it started to be more robust and be justified in the economy and in security terms.

SG-SR would have several broad mandates:

Law enforcement of system-wide laws. In Imperial space, they could be in addition to Imperial enforcement, work in conjunction with Imperial enforcement, or they could even largely shoulder the burden to allow Imperial assets (other than some inspectors/monitors) to be allocated elsewhere. Local naval elements could assist SG-SR, be an parallel structure in terms of this mandate, or direct SG-SR depending on agencies and their heirarchies. In some particularly peaceful regions, some planets may not even retain a system navy but instead have an SG-SR. There would be integration/cooperation generally with local and Imperial law enforcement around ports-of-entry, stations, and such like.
Providing security within the system - investigating crimes beyond the mainworlds, pursuing and/or deterring piracy or barratry, securing stations, high ports, and other sensitive system or Imperial assets (details would vary depending on relationship of planet and Imperial government likely via the charter that brought the planet into the Imperium). This also would include security inspections of vessels, checks on the bona fides and qualifications of ships and their crews, enforcement of safety and traffic laws at times, and setting up temporary or permanent exclusion zones (to avoid a danger for one reason, others exist) and for deploying aides to navigation as necessary and maintaining them.
Conducting Intelligence work that falls within the mandate of protecting ports, shipping, and so on related to system travel and commerce.
Search and rescue everywhere but on mainworlds - space search and rescue, search and rescue on moons, small colonies, space habitats/stations, etc. throughout the system.
In times of conflict, SG-SR vessels and personnel could be seconded to either the system navy or the Imperial Navy.
May be seconded to assist in system-related science (schlepping boffins and gear around, helping get the boffins near stellar or planetary environments without losing them, etc). This could include some periodic system surveys for any changes in the worlds/objects in the system and/or concerns that may require warnings to be posted.

What sorts of space-going assets would be involved:

Small fast response vessels - 500 tons or less - with a J-2 capacity primarily used for fast in-system deployment and evacuation of injured to stations/worlds/etc. that have better and more advanced medical options, and with a thrust of 3gs or more (once wounded are embarked, no more than 0.75 or so perceivable gravities would be applied). Likely bearing a turret or two to deter some threats, but mostly focused on medical response. High quality sensors and computers would be used to do fast, accurate searches. There would be one or more modular cutters with casualty evacuation configurations available. Would have a loaded rack of dropable traffic beacons and/or sensor platforms to increase search capacity.
Medium sized response vessels - Small hospital ship - a J-2 capacity vessel with thrust of at J-3 (again limited with wounded embarked) and that would include one or more surgical blocks (ORs, decontam, isolation, ICU and standard beds, autodocs, nurses, parameds, doctors). A few turrets just for basic deterrence, a situation room/fleet command capacity so good comms, decent to high end sensors to help in searches and coordination of larger responses. Also would have the ability to drop traffic beacons and sensor platforms. Includes multiple offloading mechanisms (cutters, straight docking, close-in assisted line crossings, etc). Would respond to more major incidents or help to coordinate many smaller vessels for a search of a lot of space/ground.
Fast Pursuit Vessels - 500 tons or less. Thrust 6 Gees, Jump 2 for similar reasons as above, full complement of weapons, high end sensors for pursuing and tracking vessels and other spacial objects that are of concern related to security or law enforcement concerns. Includes SG boarding parties who are specialists in ship boarding and inspection for security reasons. Includes at least one armed auxilliary able to deploy up to 16 boarders (two teams). These vessels would be able to help in a search with their sensors and could help with the security / traffic management during a large disaster, but would have a primary role in going after fugitives and inspecting vessels flagged as a potential threat to security.
System Tugs - J-2 wth capacity to bring back other ships on the return leg. May be over 1000 tons. May be smaller ones that can provide a real-space tow. Their job is to help get damaged or hazardous vessels or objects moved to safer places for rescue/repair/disposal.
Tender - 400 to 600 tons - for deploying and maintaining (including annual PMs) navigation aides, system sensor buoys, search platforms, science platforms, and sometimes recovering or fixing in situ smaller SG-SR vessels that have experienced serious problems that preclude them jumping of thrusting to a repair destination.

Funding would have a component derived from all corporations operating in or passing through the system (a fee charged to ships or enterprises in the system or passing through), some portion of mainworld and corporate businesses in the system (because it is a public service), and perhaps in some places, they may require payments after the fact for their services to help sustain operations.

THoughts?

“The only stable state is the one in which all men are equal before the law.” ― Aristotle