There have been many deaths in space, usually from space craft malfunctions. 

So far, no one has been murdered in space.

But given human nature, doesn't that seem inevitable as more and more people migrate to the Moon and beyond?

From Sputnik in 1957 until the first decade of the 21st century, escaping earth's atmosphere required such massive resources that only governments could attempt it. But "the privatization of space" has taken over. 

Private companies from India and Japan have landed on the moon. Private companies have put space tourists into orbit. Private companies have launched satellites in low earth orbit. Even university students have launched "cube sats" in orbit.

As this trend continues, what laws govern disputes and crimes? 

If an angry space tourist murders someone on the International Space Station, whose job is it to investigate that? 

Which nation's laws will apply if crime occurs off-planet? The ISS is co-owned by Japan, Russia, and the US. Who takes the legal lead if a Canadian astronaut is found dead in the Russian wing by a Japanese astronaut?

SpaceX has launched thousands of Starlink satellites. Unlike its government predecessors, Starlink moves fast; and in this instance, it meant they didn't bother coating their satellites with anti-reflectants. Astronomers rose a furious cry when they discovered that the shiny streaks of Starlink satellites passing by ruined all their long-exposure space photography. 

SpaceX agreed to lower the orbits of their satellites, so they didn't reflect the sun so prominently back to Earth. When they lowered their orbits, they put them precisely at the altitude US authorities had already promised Blue Origin for their coming satellite constellation. These being US companies, following ironclad tradition, everybody sued everybody else. 

Soon private companies will have competing mining claims on the Moon. How will those be resolved? Soon a private company will have its own permanent space station; who sets the rules on it? If controversial Elon Musk fulfills his life-long goal and lands a ship on Mars, who decides how government runs on an entirely unsettled planet? If a government disagreed with his rules, what the hell could they do about it when it takes nine months' journey to project physical force?

These are things I think about when hatching my next future-facing thriller. I plan to explore these issues in fiction. Not science fiction. Up-to-the-minute reality. Watch this space! (Pun intended.)