Possibly the Imperium itself directly prohibits murder only in space ("...and to bring the Rule of Law to the spaces between worlds..."), while leaving its prohibition on member worlds to member worlds. So the situation would be that it's effectively illegal everywhere, but without copying the US model of major crimes being against both state and federal law. Prosecution and punishment might vary widely between worlds.
Then I'd expect some apparatus for reporting, investigating and prosecuting serious crimes in space, but it need not be cops, judges and juries exactly as we know them. Could be an independent and smaller Bureau, could be an office internal to the Navy.
Googling it (gamings going to put me on a list if it hasn't already) I see murder is already illegal even in international waters, but we got there by countries claiming jurisdiction over anyone who's either an offender and their own national, or an offender against one of their own nationals, regardless of their home country. One article says reporting is a bigger problem than jurisdictional arguments, but it's not the case that it's not prohibited.
You could do something with that in the Imperium - yes it's illegal, but if no one reports it no investigation kicks off. (Could be an adventure hook there, a patron's friend/relative/lover hasn't come back from Belting and no one's talking, and they need one solid lead to get the authorities involved.) Or, unrelated, I was picturing Admiralty Courts with the power to try, sentence and execute, but possibly the Imperium has an office that investigates and arrests but refers offenders to member worlds for trial.
Taking low berths as a separate topic, there could be some sort of mutual aid society that registers passengers' departure, ship and intended arrival to see who makes it. If a ship or line has too many deaths they publicize it, and if passengers start disappearing without being reported as deceased they make even more of a fuss.
Almost like some sort of... Traveller's Aid Society, but minus the 1 million credit buy-in and upscale hotels, probably run by volunteers, or a couple of monks living off donations.