The Imperium MUST be able to maintain order and use force, so there is an absolute right for Imperial military units, line units or subsector forces to bear a full set of arms, and the legal forces of a planet are invited to lodge a complaint afterwards.
Law level is a bit wobbly concept in some cases when we get to the world of the Mercenary.
A merc force that imported weapons onto the planet likely did so against somebody's rules or the agreed-upon law level of the planet, and whether they are considered criminals or not will likely hinge on whether their side wins.
But with the convention of the Repatriation Bond, the mercs who lose get a ticket off the planet with no immediate repercussions (I imagine some overactive victorious governments issue sentences
in absentia, good luck enforcing it and ever get any mercs to work for that government ever again)
.
So right there we have an example of using weapons 'illegally' but due to an overall desire to end hostilities/induce surrender fast once a little war is largely decided, we have a convention where planetary law is largely flouted in the interest of a larger goal. Perhaps not an Imperial law, definitely not a warrant, but one of those unwritten customs that is 'good enough for Imperial government work'.
An interesting question is, does the Imperium have absolute right of extradition, and do planets have right of extradition or have to have treaties between them to extradite?
In the former, if so I could see an Imperial Warrant for the functional equivalent of US Marshalls being armed to the level of local LE or the target to apprehend and transport the wanted personage(s). I would probably rule that the Warrant only covers specifically capturing those people, not a blanket coverage to carry at will nor for investigative agents.
https://en.wikipedia.org/wiki/United_States_Marshals_Service
In many cases someone bad enough to merit an Imperial Warrant is likely armed, organized and/or intimidated/bribed the locals past the ability to deal with them so the local LE will likely be happy in those cases to turn over the problem to the Imps.
In the latter case, since planets have such wildly different governments and laws, I have to think that extradition treaties are necessary and would have to deal with armament of detaining/investigating agents as a matter of treaty law.
No treaty, then any armed agents have to deal with the law level like any other citizen, if caught likely deported and labelled persona non grata as a 'courtesy' assuming they didn't shoot up the place, charges pending and a diplomatic row if they did.
Now the interesting question is, if a planet has an extradition warrant/bounty out for someone's arrest and the subject is caught up to in Imperial space, what rules apply?
I should think the treaties of planetary membership would stipulate that the planetary warrants are serve-able in Imperial space, using whatever weapons are not proscribed, that the agents serving are liable to Imperial law while doing so, and that any damages incurred as part of serving the warrant are the liability of the issuing planet.
And what of the bounty hunter? I would say that there are 'officer bounties' and 'free agent bounties'.
The former are where the bounty hunter is sworn in as a deputized law officer for just that bounty and are treated by the rules as being a planetary law officer including following the rules and planet pays damages, and the latter as 'get it done any way you like, don't get caught/we don't want to know', free agent pays own liabilities.
The officer bounties should pay a lot less then the free agent bounties.
